Wu, Ai-Guo; Dong, Zhiyuan; Miao, Zibo; Mei, Jie State response and controllability for con-number-valued systems with applications to a class of quantum systems. (English) Zbl 07790015 J. Franklin Inst. 360, No. 17, 13778-13797 (2023). MSC: 93B05 81Q93 15B99 PDFBibTeX XMLCite \textit{A.-G. Wu} et al., J. Franklin Inst. 360, No. 17, 13778--13797 (2023; Zbl 07790015) Full Text: DOI
Zhang, Zijian; Chen, Xuesong Generalized conjugate direction algorithm for solving general coupled Sylvester matrix equations. (English) Zbl 1522.65063 J. Franklin Inst. 360, No. 14, 10409-10432 (2023). MSC: 65F45 15A24 PDFBibTeX XMLCite \textit{Z. Zhang} and \textit{X. Chen}, J. Franklin Inst. 360, No. 14, 10409--10432 (2023; Zbl 1522.65063) Full Text: DOI
Navarro-Moreno, Jesús; Fernández-Alcalá, Rosa María; Jiménez-López, José Domingo; Ruiz-Molina, Juan Carlos Proper adaptive filtering in four-dimensional Cayley-Dickson algebras. (English) Zbl 1520.94022 J. Franklin Inst. 360, No. 12, 7739-7769 (2023). MSC: 94A12 93E11 15A66 PDFBibTeX XMLCite \textit{J. Navarro-Moreno} et al., J. Franklin Inst. 360, No. 12, 7739--7769 (2023; Zbl 1520.94022) Full Text: DOI
Lili, Xing; Weiguo, Li; Wendi, Bao Some results for Kaczmarz method to solve Sylvester matrix equations. (English) Zbl 1518.65040 J. Franklin Inst. 360, No. 11, 7457-7461 (2023). MSC: 65F45 15A24 PDFBibTeX XMLCite \textit{X. Lili} et al., J. Franklin Inst. 360, No. 11, 7457--7461 (2023; Zbl 1518.65040) Full Text: DOI
Wang, Wenli; Qu, Gangrong; Song, Caiqin Cyclic gradient based iterative algorithm for a class of generalized coupled Sylvester-conjugate matrix equations. (English) Zbl 1516.65032 J. Franklin Inst. 360, No. 11, 7206-7229 (2023). MSC: 65F45 15A24 PDFBibTeX XMLCite \textit{W. Wang} et al., J. Franklin Inst. 360, No. 11, 7206--7229 (2023; Zbl 1516.65032) Full Text: DOI
Tan, Zhiguo; Chen, Haishan Nonlinear function activated GNN versus ZNN for online solution of general linear matrix equations. (English) Zbl 1524.65187 J. Franklin Inst. 360, No. 10, 7021-7036 (2023). MSC: 65F45 15A24 PDFBibTeX XMLCite \textit{Z. Tan} and \textit{H. Chen}, J. Franklin Inst. 360, No. 10, 7021--7036 (2023; Zbl 1524.65187) Full Text: DOI
Li, Changxi; Cheng, Daizhan Modeling, analysis, and dynamics of Bayesian games via matrix-based method. (English) Zbl 1516.91018 J. Franklin Inst. 360, No. 9, 6162-6193 (2023). MSC: 91A27 91A14 15A72 PDFBibTeX XMLCite \textit{C. Li} and \textit{D. Cheng}, J. Franklin Inst. 360, No. 9, 6162--6193 (2023; Zbl 1516.91018) Full Text: DOI
Zhang, Xin-Fang; Ding, Wei; Li, Tao Tensor form of GPBiCG algorithm for solving the generalized Sylvester quaternion tensor equations. (English) Zbl 07699703 J. Franklin Inst. 360, No. 9, 5929-5946 (2023). MSC: 65-XX 15-XX PDFBibTeX XMLCite \textit{X.-F. Zhang} et al., J. Franklin Inst. 360, No. 9, 5929--5946 (2023; Zbl 07699703) Full Text: DOI
Li, Shihai; Ma, Changfeng An improved gradient neural network for solving periodic Sylvester matrix equations. (English) Zbl 1524.65184 J. Franklin Inst. 360, No. 6, 4056-4070 (2023). MSC: 65F45 15A24 68T07 PDFBibTeX XMLCite \textit{S. Li} and \textit{C. Ma}, J. Franklin Inst. 360, No. 6, 4056--4070 (2023; Zbl 1524.65184) Full Text: DOI
Huang, Baohua; Ma, Changfeng On the minimum-norm least squares solution of the complex generalized coupled Sylvester matrix equations. (English) Zbl 1509.15009 J. Franklin Inst. 360, No. 4, 3330-3363 (2023). MSC: 15A24 65F45 PDFBibTeX XMLCite \textit{B. Huang} and \textit{C. Ma}, J. Franklin Inst. 360, No. 4, 3330--3363 (2023; Zbl 1509.15009) Full Text: DOI
G, Sowmya; V, Shankar; P, Thangavel A novel finite-time complex-valued zeoring neural network for solving time-varying complex-valued Sylvester equation. (English) Zbl 1506.93071 J. Franklin Inst. 360, No. 2, 1344-1377 (2023). MSC: 93D20 93B70 15A24 PDFBibTeX XMLCite \textit{S. G} et al., J. Franklin Inst. 360, No. 2, 1344--1377 (2023; Zbl 1506.93071) Full Text: DOI
Simos, Theodore E.; Katsikis, Vasilios N.; Mourtas, Spyridon D.; Stanimirović, Predrag S. Finite-time convergent zeroing neural network for solving time-varying algebraic Riccati equations. (English) Zbl 1504.93338 J. Franklin Inst. 359, No. 18, 10867-10883 (2022). MSC: 93D40 93C10 15B99 PDFBibTeX XMLCite \textit{T. E. Simos} et al., J. Franklin Inst. 359, No. 18, 10867--10883 (2022; Zbl 1504.93338) Full Text: DOI
Lv, Lingling; Chen, Jinbo; Zhang, Lei; Zhang, Fengrui Gradient-based neural networks for solving periodic Sylvester matrix equations. (English) Zbl 1505.65178 J. Franklin Inst. 359, No. 18, 10849-10866 (2022). MSC: 65F45 15A24 PDFBibTeX XMLCite \textit{L. Lv} et al., J. Franklin Inst. 359, No. 18, 10849--10866 (2022; Zbl 1505.65178) Full Text: DOI
Huang, Baohua; Ma, Changfeng On the relaxed gradient-based iterative methods for the generalized coupled Sylvester-transpose matrix equations. (English) Zbl 07635125 J. Franklin Inst. 359, No. 18, 10688-10725 (2022). MSC: 65-XX 15-XX PDFBibTeX XMLCite \textit{B. Huang} and \textit{C. Ma}, J. Franklin Inst. 359, No. 18, 10688--10725 (2022; Zbl 07635125) Full Text: DOI
Li, Shihai; Ma, Changfeng Factor gradient iterative algorithm for solving a class of discrete periodic Sylvester matrix equations. (English) Zbl 1503.65086 J. Franklin Inst. 359, No. 17, 9952-9970 (2022). MSC: 65F45 15A24 PDFBibTeX XMLCite \textit{S. Li} and \textit{C. Ma}, J. Franklin Inst. 359, No. 17, 9952--9970 (2022; Zbl 1503.65086) Full Text: DOI
Chen, Zebin; Chen, Xuesong Conjugate gradient-based iterative algorithm for solving generalized periodic coupled Sylvester matrix equations. (English) Zbl 07617721 J. Franklin Inst. 359, No. 17, 9925-9951 (2022). MSC: 65-XX 15-XX PDFBibTeX XMLCite \textit{Z. Chen} and \textit{X. Chen}, J. Franklin Inst. 359, No. 17, 9925--9951 (2022; Zbl 07617721) Full Text: DOI
Shafiei, Soheila Ghoroghi; Hajarian, Masoud Developing Kaczmarz method for solving Sylvester matrix equations. (English) Zbl 1503.65088 J. Franklin Inst. 359, No. 16, 8991-9005 (2022). MSC: 65F45 15A24 PDFBibTeX XMLCite \textit{S. G. Shafiei} and \textit{M. Hajarian}, J. Franklin Inst. 359, No. 16, 8991--9005 (2022; Zbl 1503.65088) Full Text: DOI
Tian, Zhaolu; Wang, Yudong; Dong, Yinghui; Wang, Shiyu New results of the IO iteration algorithm for solving Sylvester matrix equation. (English) Zbl 1502.65020 J. Franklin Inst. 359, No. 15, 8201-8217 (2022). MSC: 65F45 15A24 PDFBibTeX XMLCite \textit{Z. Tian} et al., J. Franklin Inst. 359, No. 15, 8201--8217 (2022; Zbl 1502.65020) Full Text: DOI
Shafiei, Soheila Ghoroghi; Hajarian, Masoud An iterative method based on ADMM for solving generalized Sylvester matrix equations. (English) Zbl 1508.65039 J. Franklin Inst. 359, No. 15, 8155-8170 (2022). Reviewer: Juan-Enrique Martínez-Legaz (Barcelona) MSC: 65F45 15A24 90C25 PDFBibTeX XMLCite \textit{S. G. Shafiei} and \textit{M. Hajarian}, J. Franklin Inst. 359, No. 15, 8155--8170 (2022; Zbl 1508.65039) Full Text: DOI
Erfanifar, Raziyeh; Sayevand, Khosro; Hajarian, Masoud Convergence analysis of Newton method without inversion for solving discrete algebraic Riccati equations. (English) Zbl 1502.65018 J. Franklin Inst. 359, No. 14, 7540-7561 (2022). MSC: 65F45 15A24 49M15 93C55 PDFBibTeX XMLCite \textit{R. Erfanifar} et al., J. Franklin Inst. 359, No. 14, 7540--7561 (2022; Zbl 1502.65018) Full Text: DOI
Hu, Jingjing; Ke, Yifen; Ma, Changfeng Generalized conjugate direction algorithm for solving generalized coupled Sylvester transpose matrix equations over reflexive or anti-reflexive matrices. (English) Zbl 1498.65057 J. Franklin Inst. 359, No. 13, 6958-6985 (2022). MSC: 65F45 15A24 PDFBibTeX XMLCite \textit{J. Hu} et al., J. Franklin Inst. 359, No. 13, 6958--6985 (2022; Zbl 1498.65057) Full Text: DOI
Ma, Changfeng; Yan, Tongxin A finite iterative algorithm for the general discrete-time periodic Sylvester matrix equations. (English) Zbl 1491.93025 J. Franklin Inst. 359, No. 9, 4410-4432 (2022). MSC: 93B25 93C55 15A24 PDFBibTeX XMLCite \textit{C. Ma} and \textit{T. Yan}, J. Franklin Inst. 359, No. 9, 4410--4432 (2022; Zbl 1491.93025) Full Text: DOI
Chen, Zebin; Chen, Xuesong Modification on the convergence results of the Sylvester matrix equation \(AX+XB=C\). (English) Zbl 1492.65101 J. Franklin Inst. 359, No. 7, 3126-3147 (2022). MSC: 65F45 15A24 PDFBibTeX XMLCite \textit{Z. Chen} and \textit{X. Chen}, J. Franklin Inst. 359, No. 7, 3126--3147 (2022; Zbl 1492.65101) Full Text: DOI
Shi, Yang; Pan, Zhenggang; Li, Jian; Li, Bin; Sun, Xiaobing Recurrent neural dynamics for handling linear equation system with rank-deficient coefficient and disturbance existence. (English) Zbl 07526650 J. Franklin Inst. 359, No. 7, 3090-3102 (2022). MSC: 15-XX PDFBibTeX XMLCite \textit{Y. Shi} et al., J. Franklin Inst. 359, No. 7, 3090--3102 (2022; Zbl 07526650) Full Text: DOI
Erfanifar, Raziyeh; Sayevand, Khosro; Hajarian, Masoud An efficient inversion-free method for solving the nonlinear matrix equation \(X^p + \sum_{j=1}^ma_j^*X^{-q_j}a_j=Q\). (English) Zbl 07526649 J. Franklin Inst. 359, No. 7, 3071-3089 (2022). MSC: 15-XX PDFBibTeX XMLCite \textit{R. Erfanifar} et al., J. Franklin Inst. 359, No. 7, 3071--3089 (2022; Zbl 07526649) Full Text: DOI
Liu, Aixin; Li, Haitao Matrix approach to verification of finite multi-potential games. (English) Zbl 1484.91029 J. Franklin Inst. 359, No. 5, 2229-2243 (2022). MSC: 91A14 15A72 PDFBibTeX XMLCite \textit{A. Liu} and \textit{H. Li}, J. Franklin Inst. 359, No. 5, 2229--2243 (2022; Zbl 1484.91029) Full Text: DOI
Wang, Yanjiao; Tang, Shihua; Gu, Xiaobo Parameter estimation for nonlinear Volterra systems by using the multi-innovation identification theory and tensor decomposition. (English) Zbl 1481.93022 J. Franklin Inst. 359, No. 2, 1782-1802 (2022). MSC: 93B30 93C10 15A72 PDFBibTeX XMLCite \textit{Y. Wang} et al., J. Franklin Inst. 359, No. 2, 1782--1802 (2022; Zbl 1481.93022) Full Text: DOI
Chiang, Chun-Yueh The convergence analysis of an accelerated iteration for solving algebraic Riccati equations. (English) Zbl 1489.65061 J. Franklin Inst. 359, No. 1, 619-636 (2022). Reviewer: Alain Brillard (Riedisheim) MSC: 65F45 65F10 49J45 49J21 15A24 PDFBibTeX XMLCite \textit{C.-Y. Chiang}, J. Franklin Inst. 359, No. 1, 619--636 (2022; Zbl 1489.65061) Full Text: DOI arXiv
Chen, Xuesong; Chen, Zebin An iterative algorithm for generalized periodic multiple coupled Sylvester matrix equations. (English) Zbl 1473.65049 J. Franklin Inst. 358, No. 10, 5513-5531 (2021). MSC: 65F45 15A24 65F10 PDFBibTeX XMLCite \textit{X. Chen} and \textit{Z. Chen}, J. Franklin Inst. 358, No. 10, 5513--5531 (2021; Zbl 1473.65049) Full Text: DOI
Lv, Lingling; Chen, Jinbo; Zhang, Zhe; Wang, Baowen; Zhang, Lei A numerical solution of a class of periodic coupled matrix equations. (English) Zbl 1455.65064 J. Franklin Inst. 358, No. 3, 2039-2059 (2021). MSC: 65F45 15A24 PDFBibTeX XMLCite \textit{L. Lv} et al., J. Franklin Inst. 358, No. 3, 2039--2059 (2021; Zbl 1455.65064) Full Text: DOI
Yan, Tongxin; Ma, Changfeng The BCR algorithms for solving the reflexive or anti-reflexive solutions of generalized coupled Sylvester matrix equations. (English) Zbl 1497.65078 J. Franklin Inst. 357, No. 17, 12787-12807 (2020). MSC: 65F45 15A24 PDFBibTeX XMLCite \textit{T. Yan} and \textit{C. Ma}, J. Franklin Inst. 357, No. 17, 12787--12807 (2020; Zbl 1497.65078) Full Text: DOI
Zhang, Lei; Tang, Shiyu; Lv, Lingling An finite iterative algorithm for sloving periodic Sylvester bimatrix equations. (English) Zbl 1450.93010 J. Franklin Inst. 357, No. 15, 10757-10772 (2020). MSC: 93B25 15A24 PDFBibTeX XMLCite \textit{L. Zhang} et al., J. Franklin Inst. 357, No. 15, 10757--10772 (2020; Zbl 1450.93010) Full Text: DOI
Jian, Zhen; Xiao, Lin; Li, Kenli; Zuo, Qiuyue; Zhang, Yongsheng Adaptive coefficient designs for nonlinear activation function and its application to zeroing neural network for solving time-varying Sylvester equation. (English) Zbl 1451.68226 J. Franklin Inst. 357, No. 14, 9909-9929 (2020). MSC: 68T05 15A24 65F45 93C40 PDFBibTeX XMLCite \textit{Z. Jian} et al., J. Franklin Inst. 357, No. 14, 9909--9929 (2020; Zbl 1451.68226) Full Text: DOI
Tian, Zhaolu; Wang, Junxin; Dong, Yinghui; Liu, Zhongyun A multi-step Smith-inner-outer iteration algorithm for solving coupled continuous Markovian jump Lyapunov matrix equations. (English) Zbl 1437.93128 J. Franklin Inst. 357, No. 6, 3656-3679 (2020). MSC: 93E03 15B99 PDFBibTeX XMLCite \textit{Z. Tian} et al., J. Franklin Inst. 357, No. 6, 3656--3679 (2020; Zbl 1437.93128) Full Text: DOI
Shi, Yang; Jin, Long; Li, Shuai; Qiang, Jipeng Proposing, developing and verification of a novel discrete-time zeroing neural network for solving future augmented Sylvester matrix equation. (English) Zbl 1437.93077 J. Franklin Inst. 357, No. 6, 3636-3655 (2020). MSC: 93C55 15B99 93-10 PDFBibTeX XMLCite \textit{Y. Shi} et al., J. Franklin Inst. 357, No. 6, 3636--3655 (2020; Zbl 1437.93077) Full Text: DOI Link
Lv, Lingling; Tang, Shiyu; Zhang, Lei Parametric solutions to generalized periodic Sylvester bimatrix equations. (English) Zbl 1437.93039 J. Franklin Inst. 357, No. 6, 3601-3621 (2020). MSC: 93B55 93C05 15B99 PDFBibTeX XMLCite \textit{L. Lv} et al., J. Franklin Inst. 357, No. 6, 3601--3621 (2020; Zbl 1437.93039) Full Text: DOI
Hajarian, Masoud Conjugate gradient-like methods for solving general tensor equation with Einstein product. (English) Zbl 1440.65050 J. Franklin Inst. 357, No. 7, 4272-4285 (2020). MSC: 65F45 15A24 15A69 PDFBibTeX XMLCite \textit{M. Hajarian}, J. Franklin Inst. 357, No. 7, 4272--4285 (2020; Zbl 1440.65050) Full Text: DOI
Jiao, Jianmin; Zhang, Rui An extended reciprocally convex matrix inequality and its application to stability analysis of systems with additive time-varying delays. (English) Zbl 1451.93274 J. Franklin Inst. 357, No. 4, 2282-2294 (2020). MSC: 93D05 93C43 15A45 PDFBibTeX XMLCite \textit{J. Jiao} and \textit{R. Zhang}, J. Franklin Inst. 357, No. 4, 2282--2294 (2020; Zbl 1451.93274) Full Text: DOI
Wang, Xingyuan; Gao, Suo Application of matrix semi-tensor product in chaotic image encryption. (English) Zbl 1455.94038 J. Franklin Inst. 356, No. 18, 11638-11667 (2019). MSC: 94A08 37D45 15A69 94A60 93A15 PDFBibTeX XMLCite \textit{X. Wang} and \textit{S. Gao}, J. Franklin Inst. 356, No. 18, 11638--11667 (2019; Zbl 1455.94038) Full Text: DOI
Lv, Lingling; Zhang, Zhe; Zhang, Lei; Liu, Xianxing Gradient based approach for generalized discrete-time periodic coupled Sylvester matrix equations. (English) Zbl 1398.93207 J. Franklin Inst. 355, No. 15, 7691-7705 (2018). MSC: 93C55 93C05 15A24 65F30 93B40 PDFBibTeX XMLCite \textit{L. Lv} et al., J. Franklin Inst. 355, No. 15, 7691--7705 (2018; Zbl 1398.93207) Full Text: DOI
Zhou, Bin Solutions to linear bimatrix equations with applications to pole assignment of complex-valued linear systems. (English) Zbl 1398.93133 J. Franklin Inst. 355, No. 15, 7246-7280 (2018). MSC: 93C05 93B52 93B55 93D05 15A24 93B40 PDFBibTeX XMLCite \textit{B. Zhou}, J. Franklin Inst. 355, No. 15, 7246--7280 (2018; Zbl 1398.93133) Full Text: DOI arXiv
Bishop, Adrian N.; Del Moral, Pierre On the robustness of Riccati flows to complete model misspecification. (English) Zbl 1398.93077 J. Franklin Inst. 355, No. 15, 7178-7200 (2018). MSC: 93B35 93B28 93C15 15A24 PDFBibTeX XMLCite \textit{A. N. Bishop} and \textit{P. Del Moral}, J. Franklin Inst. 355, No. 15, 7178--7200 (2018; Zbl 1398.93077) Full Text: DOI
Huang, Baohua; Ma, Changfeng The relaxed gradient-based iterative algorithms for a class of generalized coupled Sylvester-conjugate matrix equations. (English) Zbl 1395.65011 J. Franklin Inst. 355, No. 6, 3168-3195 (2018). MSC: 65F30 15A24 65F10 93B40 PDFBibTeX XMLCite \textit{B. Huang} and \textit{C. Ma}, J. Franklin Inst. 355, No. 6, 3168--3195 (2018; Zbl 1395.65011) Full Text: DOI
Yukawa, Masahiro; Kagami, Hideaki Supervised nonnegative matrix factorization via minimization of regularized Moreau-envelope of divergence function with application to music transcription. (English) Zbl 1398.65131 J. Franklin Inst. 355, No. 4, 2041-2066 (2018). MSC: 65K05 00A65 15A23 15B48 46E22 65F30 90C25 94A17 PDFBibTeX XMLCite \textit{M. Yukawa} and \textit{H. Kagami}, J. Franklin Inst. 355, No. 4, 2041--2066 (2018; Zbl 1398.65131) Full Text: DOI
Zhang, Fengxia; Wei, Musheng; Li, Ying; Zhao, Jianli The minimal norm least squares Hermitian solution of the complex matrix equation \(AXB+CXD=E\). (English) Zbl 1393.93055 J. Franklin Inst. 355, No. 3, 1296-1310 (2018). MSC: 93C05 15A24 15A09 PDFBibTeX XMLCite \textit{F. Zhang} et al., J. Franklin Inst. 355, No. 3, 1296--1310 (2018; Zbl 1393.93055) Full Text: DOI
Sheng, Xingping A relaxed gradient based algorithm for solving generalized coupled Sylvester matrix equations. (English) Zbl 1390.93305 J. Franklin Inst. 355, No. 10, 4282-4297 (2018). MSC: 93B40 15A24 PDFBibTeX XMLCite \textit{X. Sheng}, J. Franklin Inst. 355, No. 10, 4282--4297 (2018; Zbl 1390.93305) Full Text: DOI
Lv, Lingling; Zhang, Zhe Finite iterative solutions to periodic Sylvester matrix equations. (English) Zbl 1398.93365 J. Franklin Inst. 354, No. 5, 2358-2370 (2017). MSC: 93E24 15A24 65F30 PDFBibTeX XMLCite \textit{L. Lv} and \textit{Z. Zhang}, J. Franklin Inst. 354, No. 5, 2358--2370 (2017; Zbl 1398.93365) Full Text: DOI
Hajarian, Masoud Convergence of HS version of BCR algorithm to solve the generalized Sylvester matrix equation over generalized reflexive matrices. (English) Zbl 1398.93111 J. Franklin Inst. 354, No. 5, 2340-2357 (2017). MSC: 93B40 15A24 65F30 65F10 PDFBibTeX XMLCite \textit{M. Hajarian}, J. Franklin Inst. 354, No. 5, 2340--2357 (2017; Zbl 1398.93111) Full Text: DOI
Zhang, Huamin A finite iterative algorithm for solving the complex generalized coupled Sylvester matrix equations by using the linear operators. (English) Zbl 1378.93047 J. Franklin Inst. 354, No. 4, 1856-1874 (2017). MSC: 93B40 15A24 PDFBibTeX XMLCite \textit{H. Zhang}, J. Franklin Inst. 354, No. 4, 1856--1874 (2017; Zbl 1378.93047) Full Text: DOI
Huang, Chao; Yu, Changbin Uniform upper bound of the second largest eigenvalue of stochastic matrices with equal-neighbor rule. (English) Zbl 1373.93142 J. Franklin Inst. 354, No. 14, 6033-6043 (2017). MSC: 93B60 15B51 PDFBibTeX XMLCite \textit{C. Huang} and \textit{C. Yu}, J. Franklin Inst. 354, No. 14, 6033--6043 (2017; Zbl 1373.93142) Full Text: DOI
Chiang, Chun-Yueh An accelerated technique for solving the positive definite solutions of a class of nonlinear matrix equations. (English) Zbl 1373.93147 J. Franklin Inst. 354, No. 15, 7088-7118 (2017). MSC: 93C10 93B40 15A24 PDFBibTeX XMLCite \textit{C.-Y. Chiang}, J. Franklin Inst. 354, No. 15, 7088--7118 (2017; Zbl 1373.93147) Full Text: DOI
Zhang, Huamin; Yin, Hongcai New proof of the gradient-based iterative algorithm for a complex conjugate and transpose matrix equation. (English) Zbl 1373.93097 J. Franklin Inst. 354, No. 16, 7585-7603 (2017). MSC: 93B30 15A24 65F10 PDFBibTeX XMLCite \textit{H. Zhang} and \textit{H. Yin}, J. Franklin Inst. 354, No. 16, 7585--7603 (2017; Zbl 1373.93097) Full Text: DOI
Kouchaki, Samaneh; Sanei, Saeid Tensor factorisation for narrowband single channel source decomposition. (English) Zbl 1364.94133 J. Franklin Inst. 354, No. 7, 3152-3169 (2017). MSC: 94A12 93B60 15A99 PDFBibTeX XMLCite \textit{S. Kouchaki} and \textit{S. Sanei}, J. Franklin Inst. 354, No. 7, 3152--3169 (2017; Zbl 1364.94133) Full Text: DOI
Stanisławski, Rafał; Rydel, Marek; Latawiec, Krzysztof J. Modeling of discrete-time fractional-order state space systems using the balanced truncation method. (English) Zbl 1364.93438 J. Franklin Inst. 354, No. 7, 3008-3020 (2017). MSC: 93C55 93C05 26A33 15A18 15A23 93B05 93B07 PDFBibTeX XMLCite \textit{R. Stanisławski} et al., J. Franklin Inst. 354, No. 7, 3008--3020 (2017; Zbl 1364.93438) Full Text: DOI
Thanh, Nguyen T.; Niamsup, P.; Phat, Vu N. Finite-time stability of singular nonlinear switched time-delay systems: a singular value decomposition approach. (English) Zbl 1364.93742 J. Franklin Inst. 354, No. 8, 3502-3518 (2017). MSC: 93D99 93B60 93C10 15A18 PDFBibTeX XMLCite \textit{N. T. Thanh} et al., J. Franklin Inst. 354, No. 8, 3502--3518 (2017; Zbl 1364.93742) Full Text: DOI
Hajarian, Masoud Symmetric solutions of the coupled generalized Sylvester matrix equations via BCR algorithm. (English) Zbl 1344.93044 J. Franklin Inst. 353, No. 13, 3233-3248 (2016). MSC: 93B40 15A24 PDFBibTeX XMLCite \textit{M. Hajarian}, J. Franklin Inst. 353, No. 13, 3233--3248 (2016; Zbl 1344.93044) Full Text: DOI
Xu, Jianhong; Rajasingam, Prasanthan New unified matrix upper bound on the solution of the continuous coupled algebraic Riccati equation. (English) Zbl 1336.93176 J. Franklin Inst. 353, No. 5, 1233-1247 (2016). MSC: 93E20 60J75 15A24 PDFBibTeX XMLCite \textit{J. Xu} and \textit{P. Rajasingam}, J. Franklin Inst. 353, No. 5, 1233--1247 (2016; Zbl 1336.93176) Full Text: DOI
Gao, Xiangyu On the existence of solutions of the linear matrix equation \(XF-Y=0\) with the rank constraint. (English) Zbl 1336.15005 J. Franklin Inst. 353, No. 5, 1220-1232 (2016). MSC: 15A18 15A24 PDFBibTeX XMLCite \textit{X. Gao}, J. Franklin Inst. 353, No. 5, 1220--1232 (2016; Zbl 1336.15005) Full Text: DOI
Wang, Hongxing; Guo, Wenbin The minimal rank of matrix expressions with respect to Hermitian matrix-revised. (English) Zbl 1336.15010 J. Franklin Inst. 353, No. 5, 1206-1219 (2016). MSC: 15A24 15A03 PDFBibTeX XMLCite \textit{H. Wang} and \textit{W. Guo}, J. Franklin Inst. 353, No. 5, 1206--1219 (2016; Zbl 1336.15010) Full Text: DOI
Li, Wen; Xie, Ze-Jia; Vong, Seak-Weng Sensitivity analysis for the symplectic QR factorization. (English) Zbl 1336.15007 J. Franklin Inst. 353, No. 5, 1186-1205 (2016). MSC: 15A23 PDFBibTeX XMLCite \textit{W. Li} et al., J. Franklin Inst. 353, No. 5, 1186--1205 (2016; Zbl 1336.15007) Full Text: DOI
Hajarian, Masoud Extending the CGLS algorithm for least squares solutions of the generalized Sylvester-transpose matrix equations. (English) Zbl 1336.93061 J. Franklin Inst. 353, No. 5, 1168-1185 (2016). MSC: 93B40 15A24 PDFBibTeX XMLCite \textit{M. Hajarian}, J. Franklin Inst. 353, No. 5, 1168--1185 (2016; Zbl 1336.93061) Full Text: DOI
Zhang, Huamin; Ding, Feng Iterative algorithms for \(X+A^{\mathrm T}X^{-1}A=I\) by using the hierarchical identification principle. (English) Zbl 1336.93066 J. Franklin Inst. 353, No. 5, 1132-1146 (2016). MSC: 93B40 15A24 93C10 PDFBibTeX XMLCite \textit{H. Zhang} and \textit{F. Ding}, J. Franklin Inst. 353, No. 5, 1132--1146 (2016; Zbl 1336.93066) Full Text: DOI
Yao, Juan; Feng, Jun-e; Meng, Min On solutions of the matrix equation \(AX=B\) with respect to semi-tensor product. (English) Zbl 1336.15011 J. Franklin Inst. 353, No. 5, 1109-1131 (2016). MSC: 15A24 PDFBibTeX XMLCite \textit{J. Yao} et al., J. Franklin Inst. 353, No. 5, 1109--1131 (2016; Zbl 1336.15011) Full Text: DOI
Chen, Sheng; Tian, Yunbo On T-Sylvester equations over commutative rings. (English) Zbl 1336.93042 J. Franklin Inst. 353, No. 5, 1102-1108 (2016). MSC: 93B25 15A24 PDFBibTeX XMLCite \textit{S. Chen} and \textit{Y. Tian}, J. Franklin Inst. 353, No. 5, 1102--1108 (2016; Zbl 1336.93042) Full Text: DOI
Lv, Ling-Ling; Zhang, Lei Parametric solutions to the discrete periodic regulator equations. (English) Zbl 1336.93102 J. Franklin Inst. 353, No. 5, 1089-1101 (2016). MSC: 93C55 93B40 15A24 PDFBibTeX XMLCite \textit{L.-L. Lv} and \textit{L. Zhang}, J. Franklin Inst. 353, No. 5, 1089--1101 (2016; Zbl 1336.93102) Full Text: DOI
Chiang, Chun-Yueh On the Sylvester-like matrix equation \(AX+f(X)B=C\). (English) Zbl 1336.93057 J. Franklin Inst. 353, No. 5, 1061-1074 (2016). MSC: 93B40 15A24 PDFBibTeX XMLCite \textit{C.-Y. Chiang}, J. Franklin Inst. 353, No. 5, 1061--1074 (2016; Zbl 1336.93057) Full Text: DOI arXiv
Wu, Ai-Guo; Sreeram, Victor; Wu, Wei-Jun Solution to dynamic matrix linear systems by operator exponential functions. (English) Zbl 1336.93043 J. Franklin Inst. 353, No. 5, 1019-1040 (2016). MSC: 93B28 93C05 15A24 PDFBibTeX XMLCite \textit{A.-G. Wu} et al., J. Franklin Inst. 353, No. 5, 1019--1040 (2016; Zbl 1336.93043) Full Text: DOI
Zhou, Bin (ed.); Chu, Delin (ed.); Saak, Jens (ed.); Xiao, MingQing (ed.) Editorial: Matrix equations with application to control theory. (English) Zbl 1336.93009 J. Franklin Inst. 353, No. 5, 971-973 (2016). MSC: 93-06 00B15 15A24 PDFBibTeX XMLCite \textit{B. Zhou} (ed.) et al., J. Franklin Inst. 353, No. 5, 971--973 (2016; Zbl 1336.93009) Full Text: DOI
Guerra, Jeremie; Yagoubi, Mohamed; Chevrel, Philippe Mixed matrix sign function/DFT inversion method for solving parameter-dependent Riccati equation. (English) Zbl 1395.93274 J. Franklin Inst. 352, No. 12, 5611-5626 (2015). MSC: 93C30 15A24 93B40 93C95 PDFBibTeX XMLCite \textit{J. Guerra} et al., J. Franklin Inst. 352, No. 12, 5611--5626 (2015; Zbl 1395.93274) Full Text: DOI
Lee, Ju-Hong; Chao, Chia-Ching; Huang, Chia-Cheng; Lo, Wen-Chen Adaptive cyclostationary array beamforming with robust capabilities. (English) Zbl 1395.94130 J. Franklin Inst. 352, No. 6, 2486-2503 (2015). MSC: 94A12 94A14 93B40 94A05 15A09 PDFBibTeX XMLCite \textit{J.-H. Lee} et al., J. Franklin Inst. 352, No. 6, 2486--2503 (2015; Zbl 1395.94130) Full Text: DOI
Lin, Matthew M.; Chiang, Chun-Yueh A note on Sylvester-type equations. (English) Zbl 1395.93242 J. Franklin Inst. 352, No. 5, 2171-2186 (2015). MSC: 93B60 15A24 15A18 PDFBibTeX XMLCite \textit{M. M. Lin} and \textit{C.-Y. Chiang}, J. Franklin Inst. 352, No. 5, 2171--2186 (2015; Zbl 1395.93242) Full Text: DOI arXiv
Chen, Sheng; Tian, Yunbo On solutions of generalized Sylvester equation in polynomial matrices. (English) Zbl 1398.65078 J. Franklin Inst. 351, No. 12, 5376-5385 (2014). MSC: 65F30 15A24 PDFBibTeX XMLCite \textit{S. Chen} and \textit{Y. Tian}, J. Franklin Inst. 351, No. 12, 5376--5385 (2014; Zbl 1398.65078) Full Text: DOI
Yuan, Shifang; Liao, Anping Least squares Hermitian solution of the complex matrix equation \(AXB+CXD=E\) with the least norm. (English) Zbl 1307.93175 J. Franklin Inst. 351, No. 11, 4978-4997 (2014). MSC: 15A24 65F45 PDFBibTeX XMLCite \textit{S. Yuan} and \textit{A. Liao}, J. Franklin Inst. 351, No. 11, 4978--4997 (2014; Zbl 1307.93175) Full Text: DOI
Zhang, Huamin; Ding, Feng A property of the eigenvalues of the symmetric positive definite matrix and the iterative algorithm for coupled Sylvester matrix equations. (English) Zbl 1293.15006 J. Franklin Inst. 351, No. 1, 340-357 (2014). MSC: 15A18 15A24 65F10 PDFBibTeX XMLCite \textit{H. Zhang} and \textit{F. Ding}, J. Franklin Inst. 351, No. 1, 340--357 (2014; Zbl 1293.15006) Full Text: DOI
Hajarian, Masoud Matrix iterative methods for solving the Sylvester-transpose and periodic Sylvester matrix equations. (English) Zbl 1293.93289 J. Franklin Inst. 350, No. 10, 3328-3341 (2013). MSC: 93B40 15A24 PDFBibTeX XMLCite \textit{M. Hajarian}, J. Franklin Inst. 350, No. 10, 3328--3341 (2013; Zbl 1293.93289) Full Text: DOI
Zhu, Shuqian; Meng, Min; Zhang, Chenghui Exponential stability for positive systems with bounded time-varying delays and static output feedback stabilization. (English) Zbl 1269.93088 J. Franklin Inst. 350, No. 3, 617-636 (2013). MSC: 93D15 93D20 15B48 93C55 90C05 PDFBibTeX XMLCite \textit{S. Zhu} et al., J. Franklin Inst. 350, No. 3, 617--636 (2013; Zbl 1269.93088) Full Text: DOI Link
Xue, Mengran; Roy, Sandip Spectral and graph-theoretic bounds on steady-state-probability estimation performance for an ergodic Markov chain. (English) Zbl 1274.62552 J. Franklin Inst. 348, No. 9, 2448-2467 (2011). MSC: 62M05 15B51 60J10 PDFBibTeX XMLCite \textit{M. Xue} and \textit{S. Roy}, J. Franklin Inst. 348, No. 9, 2448--2467 (2011; Zbl 1274.62552) Full Text: DOI
Forbes, James Richard; Damaren, Christopher John Design of optimal strictly positive real controllers using numerical optimization for the control of flexible robotic systems. (English) Zbl 1231.93062 J. Franklin Inst. 348, No. 8, 2191-2215 (2011). MSC: 93C85 49N90 15B48 93C35 PDFBibTeX XMLCite \textit{J. R. Forbes} and \textit{C. J. Damaren}, J. Franklin Inst. 348, No. 8, 2191--2215 (2011; Zbl 1231.93062) Full Text: DOI
Liu, Jianzhou; Zhang, Juan; Liu, Yu New solution bounds for the continuous algebraic Riccati equation. (English) Zbl 1259.15021 J. Franklin Inst. 348, No. 8, 2128-2141 (2011). Reviewer: Jaroslav Zemánek (Warszawa) MSC: 15A24 15A18 15A42 PDFBibTeX XMLCite \textit{J. Liu} et al., J. Franklin Inst. 348, No. 8, 2128--2141 (2011; Zbl 1259.15021) Full Text: DOI
Ding, Xiuyong; Shu, Lan; Liu, Xiu On linear copositive Lyapunov functions for switched positive systems. (English) Zbl 1231.93058 J. Franklin Inst. 348, No. 8, 2099-2107 (2011). MSC: 93C55 15B48 PDFBibTeX XMLCite \textit{X. Ding} et al., J. Franklin Inst. 348, No. 8, 2099--2107 (2011; Zbl 1231.93058) Full Text: DOI
Lee, Chien-Hua; Chen, Cheng-Yi Matrix solution bounds of the continuous Lyapunov equation by using a bilinear transformation. (English) Zbl 1298.15020 J. Franklin Inst. 346, No. 8, 741-751 (2009). MSC: 15A24 93D05 PDFBibTeX XMLCite \textit{C.-H. Lee} and \textit{C.-Y. Chen}, J. Franklin Inst. 346, No. 8, 741--751 (2009; Zbl 1298.15020) Full Text: DOI
De la Sen, M. On the excitability of a class of positive continuous time-delay systems. (English) Zbl 1298.93178 J. Franklin Inst. 346, No. 7, 705-729 (2009). MSC: 93C05 15B48 PDFBibTeX XMLCite \textit{M. De la Sen}, J. Franklin Inst. 346, No. 7, 705--729 (2009; Zbl 1298.93178) Full Text: DOI
Chadli, Mohammed; Akhenak, A.; Ragot, J.; Maquin, D. State and unknown input estimation for discrete time multiple model. (English) Zbl 1169.93361 J. Franklin Inst. 346, No. 6, 593-610 (2009). MSC: 93C55 93C10 93B55 15A39 PDFBibTeX XMLCite \textit{M. Chadli} et al., J. Franklin Inst. 346, No. 6, 593--610 (2009; Zbl 1169.93361) Full Text: DOI
Tian, Yongge Some properties of submatrices in a solution to the matrix equation \(AXB=C\) with applications. (English) Zbl 1168.15307 J. Franklin Inst. 346, No. 6, 557-569 (2009). MSC: 15A24 15A03 15A09 PDFBibTeX XMLCite \textit{Y. Tian}, J. Franklin Inst. 346, No. 6, 557--569 (2009; Zbl 1168.15307) Full Text: DOI
Hutu, Florin; Cauet, Sebastien; Coirault, Patrick Robust synchronization of different coupled oscillators: application to antenna arrays. (English) Zbl 1167.93333 J. Franklin Inst. 346, No. 5, 413-430 (2009). MSC: 93B35 78A50 93D05 93D20 93C15 90B18 15A39 93C10 PDFBibTeX XMLCite \textit{F. Hutu} et al., J. Franklin Inst. 346, No. 5, 413--430 (2009; Zbl 1167.93333) Full Text: DOI HAL
Peng, Chen; Yue, Dong; Tian, Engang; Gu, Zhou A delay distribution based stability analysis and synthesis approach for networked control systems. (English) Zbl 1166.93381 J. Franklin Inst. 346, No. 4, 349-365 (2009). MSC: 93E15 90B15 15A39 PDFBibTeX XMLCite \textit{C. Peng} et al., J. Franklin Inst. 346, No. 4, 349--365 (2009; Zbl 1166.93381) Full Text: DOI
Xu, Jianming; Yu, Li Delay-dependent guaranteed cost control for uncertain 2-D discrete systems with state delay in the FM second model. (English) Zbl 1160.93383 J. Franklin Inst. 346, No. 2, 159-174 (2009). MSC: 93D15 93C55 15A39 PDFBibTeX XMLCite \textit{J. Xu} and \textit{L. Yu}, J. Franklin Inst. 346, No. 2, 159--174 (2009; Zbl 1160.93383) Full Text: DOI
Zhou, Shaosheng; Zheng, Wei Xing Robust \(H_\infty \)-control of delayed singular systems with linear fractional parametric uncertainties. (English) Zbl 1160.93330 J. Franklin Inst. 346, No. 2, 147-158 (2009). MSC: 93B36 93B35 15A39 93C15 PDFBibTeX XMLCite \textit{S. Zhou} and \textit{W. X. Zheng}, J. Franklin Inst. 346, No. 2, 147--158 (2009; Zbl 1160.93330) Full Text: DOI
Wu, Ligang; Wang, Changhong; Zeng, Qingshuang Observer-based sliding mode control for a class of uncertain nonlinear neutral delay systems. (English) Zbl 1167.93326 J. Franklin Inst. 345, No. 3, 233-253 (2008). MSC: 93B12 93C10 15A39 93D20 PDFBibTeX XMLCite \textit{L. Wu} et al., J. Franklin Inst. 345, No. 3, 233--253 (2008; Zbl 1167.93326) Full Text: DOI
Piao, Fengxian; Zhang, Qingling; Wang, Zhefeng The solution to matrix equation \(AX+X^TC=B\). (English) Zbl 1171.15015 J. Franklin Inst. 344, No. 8, 1056-1062 (2007). Reviewer: Qing-Wen Wang (Shanghai) MSC: 15A24 15A09 PDFBibTeX XMLCite \textit{F. Piao} et al., J. Franklin Inst. 344, No. 8, 1056--1062 (2007; Zbl 1171.15015) Full Text: DOI
He, P. R.; Zhang, W. J.; Li, Q. Some further development on the eigensystem approach for graph isomorphism detection. (English) Zbl 1074.05059 J. Franklin Inst. 342, No. 6, 657-673 (2005). MSC: 05C50 05C60 15A18 70B15 PDFBibTeX XMLCite \textit{P. R. He} et al., J. Franklin Inst. 342, No. 6, 657--673 (2005; Zbl 1074.05059) Full Text: DOI
Kim, Jong Hae New design method on memoryless \(H_{\infty}\) control for singular systems with delayed state and control using LMI. (English) Zbl 1063.93017 J. Franklin Inst. 342, No. 3, 321-327 (2005). MSC: 93B36 34A09 93C23 15A39 93B51 PDFBibTeX XMLCite \textit{J. H. Kim}, J. Franklin Inst. 342, No. 3, 321--327 (2005; Zbl 1063.93017) Full Text: DOI
Xu, Shengyuan; Lu, Junwei; Zhou, Shaosheng; Yang, Chengwu Design of observers for a class of discrete-time uncertain nonlinear systems with time delay. (English) Zbl 1073.93007 J. Franklin Inst. 341, No. 3, 295-308 (2004). Reviewer: Alexandra Rodkina (Kingston/Jamaica) MSC: 93B07 93B51 93C55 93C10 15A39 93D20 PDFBibTeX XMLCite \textit{S. Xu} et al., J. Franklin Inst. 341, No. 3, 295--308 (2004; Zbl 1073.93007) Full Text: DOI
Chen, Wu-Hua; Guan, Zhi-Hong; Lu, Xiaomei Delay-dependent guaranteed cost control for uncertain discrete-time systems with both state and input delays. (English) Zbl 1055.93054 J. Franklin Inst. 341, No. 5, 419-430 (2004). MSC: 93C55 15A39 PDFBibTeX XMLCite \textit{W.-H. Chen} et al., J. Franklin Inst. 341, No. 5, 419--430 (2004; Zbl 1055.93054) Full Text: DOI
Kim, Kyung-Soo; Jabbari, Faryar Disturbance attenuation via strictly positive real compensators. (English) Zbl 1037.93062 J. Franklin Inst. 340, No. 6-7, 515-521 (2003). Reviewer: Didier Henrion (Toulouse) MSC: 93C73 93B51 15A39 93B40 PDFBibTeX XMLCite \textit{K.-S. Kim} and \textit{F. Jabbari}, J. Franklin Inst. 340, No. 6--7, 515--521 (2003; Zbl 1037.93062) Full Text: DOI
Lee, C. H. Further results on the measurement of solution bounds of the generalized Lyapunov equations. (English) Zbl 1042.93029 J. Franklin Inst. 340, No. 6-7, 461-480 (2003). Reviewer: L. Rodman (Williamsburg) MSC: 93B60 15A24 PDFBibTeX XMLCite \textit{C. H. Lee}, J. Franklin Inst. 340, No. 6--7, 461--480 (2003; Zbl 1042.93029) Full Text: DOI
Cao, Yong-Yan; Lam, James; Hu, Lisheng Delay-dependent stochastic stability and \(H_{\infty}\) analysis for time-delay systems with Markovian jumping parameters. (English) Zbl 1040.93068 J. Franklin Inst. 340, No. 6-7, 423-434 (2003). Reviewer: Yuliya S. Mishura (Kyïv) MSC: 93E15 93C23 60J75 93B36 15A39 34K50 PDFBibTeX XMLCite \textit{Y.-Y. Cao} et al., J. Franklin Inst. 340, No. 6--7, 423--434 (2003; Zbl 1040.93068) Full Text: DOI
Choi, Han Ho On the uncertain variable structure systems with bounded controllers. (English) Zbl 1023.93014 J. Franklin Inst. 340, No. 2, 135-146 (2003). Reviewer: M.I.Krastanov (Sofia) MSC: 93B12 93D20 15A39 PDFBibTeX XMLCite \textit{H. H. Choi}, J. Franklin Inst. 340, No. 2, 135--146 (2003; Zbl 1023.93014) Full Text: DOI
Li, Zhihu; Wang, Jingcheng; Shao, Huihe Delay-dependent dissipative control for linear time-delay systems. (English) Zbl 1048.93050 J. Franklin Inst. 339, No. 6-7, 529-542 (2002). MSC: 93C23 15A39 PDFBibTeX XMLCite \textit{Z. Li} et al., J. Franklin Inst. 339, No. 6--7, 529--542 (2002; Zbl 1048.93050) Full Text: DOI
Yu, Li; Gao, Furong Optimal guarenteed cost control of discrete-time uncertain systems with both state and input delays. (English) Zbl 0998.93512 J. Franklin Inst. 338, No. 1, 101-110 (2001). MSC: 93C55 49N10 15A39 93C41 PDFBibTeX XMLCite \textit{L. Yu} and \textit{F. Gao}, J. Franklin Inst. 338, No. 1, 101--110 (2001; Zbl 0998.93512) Full Text: DOI