Gong, Deren; Wang, Xiaoliang; Wu, Shufan; Zhu, Xiaodan Discrete Legendre polynomials-based inequality for stability of time-varying delayed systems. (English) Zbl 1423.93288 J. Franklin Inst. 356, No. 16, 9907-9927 (2019). MSC: 93D05 42C10 PDFBibTeX XMLCite \textit{D. Gong} et al., J. Franklin Inst. 356, No. 16, 9907--9927 (2019; Zbl 1423.93288) Full Text: DOI
Lee, Seok Young; Lee, Won Il; Park, PooGyeon Orthogonal-polynomials-based integral inequality and its applications to systems with additive time-varying delays. (English) Zbl 1380.93223 J. Franklin Inst. 355, No. 1, 421-435 (2018). MSC: 93D99 93B40 PDFBibTeX XMLCite \textit{S. Y. Lee} et al., J. Franklin Inst. 355, No. 1, 421--435 (2018; Zbl 1380.93223) Full Text: DOI
Gong, Cheng; Zhang, Xian; Wu, Ligang Multiple-integral inequalities to stability analysis of linear time-delay systems. (English) Zbl 1355.93170 J. Franklin Inst. 354, No. 3, 1446-1463 (2017). MSC: 93D99 93C05 PDFBibTeX XMLCite \textit{C. Gong} et al., J. Franklin Inst. 354, No. 3, 1446--1463 (2017; Zbl 1355.93170) Full Text: DOI
Qi, Zhen-Zhong; Jiang, Yao-Lin; Xiao, Zhi-Hua Model order reduction based on general orthogonal polynomials in the time domain for coupled systems. (English) Zbl 1291.93062 J. Franklin Inst. 351, No. 6, 3200-3214 (2014). MSC: 93B11 93D99 PDFBibTeX XMLCite \textit{Z.-Z. Qi} et al., J. Franklin Inst. 351, No. 6, 3200--3214 (2014; Zbl 1291.93062) Full Text: DOI
Antić, Dragan; Danković, Bratislav; Nikolić, Saša; Milojković, Marko; Jovanović, Zoran Approximation based on orthogonal and almost orthogonal functions. (English) Zbl 1258.42028 J. Franklin Inst. 349, No. 1, 323-336 (2012). Reviewer: Enji Sato (Yamagata) MSC: 42C10 42C05 PDFBibTeX XMLCite \textit{D. Antić} et al., J. Franklin Inst. 349, No. 1, 323--336 (2012; Zbl 1258.42028) Full Text: DOI
Wang, Ren-Hong; Dan, Wei Improved Haar and Walsh functions over triangular domains. (English) Zbl 1205.42028 J. Franklin Inst. 347, No. 9, 1782-1794 (2010). MSC: 42C10 42C30 41A30 PDFBibTeX XMLCite \textit{R.-H. Wang} and \textit{W. Dan}, J. Franklin Inst. 347, No. 9, 1782--1794 (2010; Zbl 1205.42028) Full Text: DOI
Deb, Anish; Sarkar, Gautam; Biswas, Amitava; Mandal, Priyaranjan Numerical instability of deconvolution operation via block pulse functions. (English) Zbl 1151.93012 J. Franklin Inst. 345, No. 4, 319-327 (2008). MSC: 93B30 42C10 PDFBibTeX XMLCite \textit{A. Deb} et al., J. Franklin Inst. 345, No. 4, 319--327 (2008; Zbl 1151.93012) Full Text: DOI
Bokhari, M. A. Gauss quadrature formula: An extension via interpolating orthogonal polynomials. (English) Zbl 1269.65025 J. Franklin Inst. 344, No. 5, 637-645 (2007). MSC: 65D32 PDFBibTeX XMLCite \textit{M. A. Bokhari}, J. Franklin Inst. 344, No. 5, 637--645 (2007; Zbl 1269.65025) Full Text: DOI Link
Deb, Anish; Dasgupta, Anindita; Sarkar, Gautam A new set of orthogonal functions and its application to the analysis of dynamic systems. (English) Zbl 1173.33306 J. Franklin Inst. 343, No. 1, 1-26 (2006). MSC: 33C47 PDFBibTeX XMLCite \textit{A. Deb} et al., J. Franklin Inst. 343, No. 1, 1--26 (2006; Zbl 1173.33306) Full Text: DOI
Ong, S. H. Probabilistic proof of a Hankel transform of Laguerre polynomials. (English) Zbl 0965.44001 J. Franklin Inst. 336, No. 6, 1007-1011 (1999). MSC: 44A20 33C45 65C05 65R10 PDFBibTeX XMLCite \textit{S. H. Ong}, J. Franklin Inst. 336, No. 6, 1007--1011 (1999; Zbl 0965.44001) Full Text: DOI
Lee, P. A. Random deletion model and Rainville’s generating function for the Laguerre polynomials. (English) Zbl 0993.33006 J. Franklin Inst. 335B, No. 7, 1171-1175 (1998). Reviewer: Arun Kumar Agarwal (Grambling) MSC: 33C45 60E05 60E99 PDFBibTeX XMLCite \textit{P. A. Lee}, J. Franklin Inst. 335B, No. 7, 1171--1175 (1998; Zbl 0993.33006) Full Text: DOI
Mohan, B. M.; Datta, K. B. On the optimal control of linear discrete-time systems via discrete orthogonal functions. (English) Zbl 0909.49019 J. Franklin Inst. 335B, No. 4, 731-738 (1998). MSC: 49N10 93C55 33C45 PDFBibTeX XMLCite \textit{B. M. Mohan} and \textit{K. B. Datta}, J. Franklin Inst. 335B, No. 4, 731--738 (1998; Zbl 0909.49019) Full Text: DOI
Deb, Anish; Sarkar, Gautam; Bhattacharjee, Manabrata; Sen, Sunit K. All-integrator approach to linear SISO control system analysis using block pulse functions (BPF). (English) Zbl 0874.93050 J. Franklin Inst. 334B, No. 2, 319-335 (1997). Reviewer: Xu Ningshou (Beijing) MSC: 93C05 93B40 42C05 65D25 PDFBibTeX XMLCite \textit{A. Deb} et al., J. Franklin Inst. 334B, No. 2, 319--335 (1997; Zbl 0874.93050) Full Text: DOI
Ragot, José; Ekongolo, Simon; Maquin, Didier State equations and decomposition into Laguerre functions. (English) Zbl 0848.93023 J. Franklin Inst. 333B, No. 2, 283-288 (1996). MSC: 93B40 33C45 93C05 PDFBibTeX XMLCite \textit{J. Ragot} et al., J. Franklin Inst. 333B, No. 2, 283--288 (1996; Zbl 0848.93023) Full Text: DOI
Agrawal, Om Prakash A general orthogonal polynomial approach to the sensitivity analysis of linear systems. (English) Zbl 0825.93284 J. Franklin Inst. 330, No. 2, 243-258 (1993). MSC: 93C05 42C05 PDFBibTeX XMLCite \textit{O. P. Agrawal}, J. Franklin Inst. 330, No. 2, 243--258 (1993; Zbl 0825.93284) Full Text: DOI
Paraskevopoulos, P. N.; Sklavounos, P. G.; Georgiou, G. Ch. The operational matrix of integration for Bessel functions. (English) Zbl 0717.93012 J. Franklin Inst. 327, No. 2, 329-341 (1990). MSC: 93B28 42C10 93B30 PDFBibTeX XMLCite \textit{P. N. Paraskevopoulos} et al., J. Franklin Inst. 327, No. 2, 329--341 (1990; Zbl 0717.93012) Full Text: DOI
Razzaghi, Mohsen; Razzaghi, Mehdi Solution of linear two-point boundary value problems and optimal control of time-varying systems by shifted Chebyshev approximations. (English) Zbl 0714.49032 J. Franklin Inst. 327, No. 2, 321-328 (1990). MSC: 49M15 49N05 65L10 42C05 49J15 65K10 PDFBibTeX XMLCite \textit{M. Razzaghi} and \textit{M. Razzaghi}, J. Franklin Inst. 327, No. 2, 321--328 (1990; Zbl 0714.49032) Full Text: DOI
Razzaghi, Mohsen; Razzaghi, Mehdi Instabilities in the solution of a heat conduction problem using Taylor series and alternative approaches. (English) Zbl 0684.34012 J. Franklin Inst. 326, No. 5, 683-690 (1989). MSC: 34A45 42C05 PDFBibTeX XMLCite \textit{M. Razzaghi} and \textit{M. Razzaghi}, J. Franklin Inst. 326, No. 5, 683--690 (1989; Zbl 0684.34012) Full Text: DOI
Shyu, Kuo-Kai; Hwang, Chyi Optimal control of linear time-varying discrete systems via discrete Legendre orthogonal polynomials. (English) Zbl 0651.93044 J. Franklin Inst. 325, No. 4, 509-525 (1988). MSC: 93C55 44A55 33C45 93C05 PDFBibTeX XMLCite \textit{K.-K. Shyu} and \textit{C. Hwang}, J. Franklin Inst. 325, No. 4, 509--525 (1988; Zbl 0651.93044) Full Text: DOI
Hwang, Chyi; Shyu, Kuo-Kai Analysis of time-varying discrete systems using discrete Legendre orthogonal polynomials. (English) Zbl 0624.93040 J. Franklin Inst. 324, 149-164 (1987). MSC: 93C55 44A55 33C45 93C05 PDFBibTeX XMLCite \textit{C. Hwang} and \textit{K.-K. Shyu}, J. Franklin Inst. 324, 149--164 (1987; Zbl 0624.93040) Full Text: DOI
Chou, Jyh-Horng; Horng, Ing-Rong New approach to the optimal control of delay systems via Chebyshev series. (English) Zbl 0619.93043 J. Franklin Inst. 323, 95-102 (1987). MSC: 93C30 34K35 42C10 33C45 44A45 93C05 PDFBibTeX XMLCite \textit{J.-H. Chou} and \textit{I.-R. Horng}, J. Franklin Inst. 323, 95--102 (1987; Zbl 0619.93043) Full Text: DOI
Kekkeris, G. T. Chebyshev series approach to linear systems sensitivity analysis. (English) Zbl 0614.93018 J. Franklin Inst. 323, 273-283 (1987). MSC: 93B35 42C10 93C05 33C45 44A45 93C15 PDFBibTeX XMLCite \textit{G. T. Kekkeris}, J. Franklin Inst. 323, 273--283 (1987; Zbl 0614.93018) Full Text: DOI
Chou, Jyh-Horng; Horng, Ing-Rong Identification of time-varying bilinear systems using Legendre series. (English) Zbl 0606.93025 J. Franklin Inst. 322, 353-359 (1986). MSC: 93B30 42C10 93C10 33C45 44A45 PDFBibTeX XMLCite \textit{J.-H. Chou} and \textit{I.-R. Horng}, J. Franklin Inst. 322, 353--359 (1986; Zbl 0606.93025) Full Text: DOI
Sparis, Panagiotis D.; Mouroutsos, Spyridon G. Output sensitivity analysis of time-invariant linear systems using polynomial series. (English) Zbl 0605.93017 J. Franklin Inst. 321, 325-336 (1986). MSC: 93B35 42C10 93C05 33C45 44A45 PDFBibTeX XMLCite \textit{P. D. Sparis} and \textit{S. G. Mouroutsos}, J. Franklin Inst. 321, 325--336 (1986; Zbl 0605.93017) Full Text: DOI
Kamat, P. S. A simplified stability test for 1-D discrete systems. (English) Zbl 0588.93062 J. Franklin Inst. 321, 193-201 (1986). MSC: 93D99 30B70 93C55 30C15 33C45 93B17 PDFBibTeX XMLCite \textit{P. S. Kamat}, J. Franklin Inst. 321, 193--201 (1986; Zbl 0588.93062) Full Text: DOI
Lee, Tsu-Tian; Tsay, Shuh-Chuan; Horng, Ing-Rong Shifted-Jacobi series analysis of linear optimal control systems incorporating observers. (English) Zbl 0585.93027 J. Franklin Inst. 321, 289-298 (1986). MSC: 93C05 42C10 44A45 33C45 93C99 PDFBibTeX XMLCite \textit{T.-T. Lee} et al., J. Franklin Inst. 321, 289--298 (1986; Zbl 0585.93027) Full Text: DOI
Marszałek, Wiesław Analysis of bilinear systems with Picard’s method and block-pulse operational matrices. (English) Zbl 0581.93029 J. Franklin Inst. 320, 105-109 (1985). MSC: 93C10 34A45 42C10 33C45 44A45 93C15 PDFBibTeX XMLCite \textit{W. Marszałek}, J. Franklin Inst. 320, 105--109 (1985; Zbl 0581.93029) Full Text: DOI
Mouroutsos, S. G.; Paraskevopoulos, P. N. Identification of time-varying linear systems using orthogonal functions. (English) Zbl 0576.93020 J. Franklin Inst. 320, 249-258 (1985). MSC: 93B30 42C10 93C05 33C45 44A45 93C99 PDFBibTeX XMLCite \textit{S. G. Mouroutsos} and \textit{P. N. Paraskevopoulos}, J. Franklin Inst. 320, 249--258 (1985; Zbl 0576.93020) Full Text: DOI
Hwang, Chyi; Guo, Tongyi Parameter identification of a class of time-varying systems via orthogonal shifted Legendre polynomials. (English) Zbl 0589.93012 J. Franklin Inst. 318, 59-69 (1984). Reviewer: P.Paraskevopoulos MSC: 93B30 42C10 93C99 33C45 65F20 93B40 93C05 PDFBibTeX XMLCite \textit{C. Hwang} and \textit{T. Guo}, J. Franklin Inst. 318, 59--69 (1984; Zbl 0589.93012)
Mertzios, B. G. Solution and identification of discrete state-space equations via Walsh functions. (English) Zbl 0549.93037 J. Franklin Inst. 318, 383-391 (1984). MSC: 93C55 44A55 93B30 42C10 93C05 93C99 93C35 PDFBibTeX XMLCite \textit{B. G. Mertzios}, J. Franklin Inst. 318, 383--391 (1984; Zbl 0549.93037) Full Text: DOI
Tsai, Mingjong; Chen, Cha’okuang; Kung, Fanchu Analysis of linear time-varying systems by shifted Legendre polynomials. (English) Zbl 0544.93048 J. Franklin Inst. 318, 275-282 (1984). MSC: 93C99 42C10 93C05 33C45 93B17 PDFBibTeX XMLCite \textit{M. Tsai} et al., J. Franklin Inst. 318, 275--282 (1984; Zbl 0544.93048) Full Text: DOI
Hwang, Chyi Solution of a scaled system via Chebyshev polynomials. (English) Zbl 0543.93032 J. Franklin Inst. 318, 233-241 (1984). MSC: 93C15 33C45 34K05 42C10 PDFBibTeX XMLCite \textit{C. Hwang}, J. Franklin Inst. 318, 233--241 (1984; Zbl 0543.93032) Full Text: DOI
Liu, Chengchiian; Shih, Yenping Analysis and parameter estimation of bilinear systems via Chebyshev polynomials. (English) Zbl 0538.93030 J. Franklin Inst. 317, 373-382 (1984). MSC: 93C10 33C45 93C99 42C10 44A45 93B30 PDFBibTeX XMLCite \textit{C. Liu} and \textit{Y. Shih}, J. Franklin Inst. 317, 373--382 (1984; Zbl 0538.93030) Full Text: DOI
Paraskevopoulos, P. N. Chebyshev series approach to system identification, analysis and optimal control. (English) Zbl 0538.93013 J. Franklin Inst. 316, 135-157 (1983). Reviewer: N.Christov MSC: 93B30 33C45 93B50 42C10 93B40 93C05 93C99 PDFBibTeX XMLCite \textit{P. N. Paraskevopoulos}, J. Franklin Inst. 316, 135--157 (1983; Zbl 0538.93013) Full Text: DOI
Fettis, Henry E. Extension of a result of Ainsworth and Liu. (English) Zbl 0529.33010 J. Franklin Inst. 316, 191-192 (1983). MSC: 33C45 33C55 PDFBibTeX XMLCite \textit{H. E. Fettis}, J. Franklin Inst. 316, 191--192 (1983; Zbl 0529.33010) Full Text: DOI
Kung, Fan-Chu; Lee, Hua Solution of linear state-space equations and parameter estimation in feedback systems using Laguerre polynomial expansion. (English) Zbl 0502.93032 J. Franklin Inst. 314, 393-403 (1982). MSC: 93C05 42C10 93B30 93C99 PDFBibTeX XMLCite \textit{F.-C. Kung} and \textit{H. Lee}, J. Franklin Inst. 314, 393--403 (1982; Zbl 0502.93032) Full Text: DOI
Maqusi, Mohammad Identification of Volterra kernels of a class of nonlinear systems by Walsh function techniques. (English) Zbl 0449.93015 J. Franklin Inst. 310, 65-75 (1980). MSC: 93B30 93C10 42C10 PDFBibTeX XMLCite \textit{M. Maqusi}, J. Franklin Inst. 310, 65--75 (1980; Zbl 0449.93015) Full Text: DOI
Johnson, David E.; Johnson, Johnny R. Special functions of circuits and systems. (English) Zbl 0409.94026 J. Franklin Inst. 307, 95-105 (1979). Reviewer: David P. Brown MSC: 94C05 33C55 33C45 94A15 05C30 PDFBibTeX XMLCite \textit{D. E. Johnson} and \textit{J. R. Johnson}, J. Franklin Inst. 307, 95--105 (1979; Zbl 0409.94026) Full Text: DOI
Lee, P. A. Canonical expansion of a mixed bivariate distribution with negative binomial and gamma marginals. (English) Zbl 0405.62012 J. Franklin Inst. 307, 331-339 (1979). MSC: 62E15 62H10 60E99 PDFBibTeX XMLCite \textit{P. A. Lee}, J. Franklin Inst. 307, 331--339 (1979; Zbl 0405.62012) Full Text: DOI
Chen, C. F.; Tsay, Y. T.; Wu, T. T. Walsh operational matrices for fractional calculus and their application to distributed systems. (English) Zbl 0377.42004 J. Franklin Inst. 303, 267-284 (1977). MSC: 42C10 PDFBibTeX XMLCite \textit{C. F. Chen} et al., J. Franklin Inst. 303, 267--284 (1977; Zbl 0377.42004) Full Text: DOI
Chen, C. F.; Hsiao, C. H. A Walsh series direct method for solving variational problems. (English) Zbl 0339.49017 J. Franklin Inst. 300, 265-280 (1975). MSC: 49M15 33E99 42C10 PDFBibTeX XMLCite \textit{C. F. Chen} and \textit{C. H. Hsiao}, J. Franklin Inst. 300, 265--280 (1975; Zbl 0339.49017) Full Text: DOI
Jury, E. I.; Ahn, S. M. On orthogonal polynomials. (English) Zbl 0319.33017 J. Franklin Inst. 300, 169-173 (1975). MSC: 33C45 30C15 30C10 15A24 PDFBibTeX XMLCite \textit{E. I. Jury} and \textit{S. M. Ahn}, J. Franklin Inst. 300, 169--173 (1975; Zbl 0319.33017) Full Text: DOI
Ainsworth, O. R.; Liu, C. K. An interesting property of Legendre polynomials. (English) Zbl 0307.33007 J. Franklin Inst. 298, 71-72 (1974). MSC: 33C55 33C45 PDFBibTeX XMLCite \textit{O. R. Ainsworth} and \textit{C. K. Liu}, J. Franklin Inst. 298, 71--72 (1974; Zbl 0307.33007) Full Text: DOI
Levan, N. Characterization of a class of lossy n-port networks. (English) Zbl 0277.94017 J. Franklin Inst. 294, 13-21 (1972). MSC: 94C10 42C05 PDFBibTeX XMLCite \textit{N. Levan}, J. Franklin Inst. 294, 13--21 (1972; Zbl 0277.94017) Full Text: DOI
Sox, J. L.; Harrington, W. J. Some orthogonal functions which are linear combinations of square-wave functions. (English) Zbl 0253.42015 J. Franklin Inst. 288, 42-48 (1969). MSC: 42C10 33C45 PDFBibTeX XMLCite \textit{J. L. Sox} and \textit{W. J. Harrington}, J. Franklin Inst. 288, 42--48 (1969; Zbl 0253.42015) Full Text: DOI