×

zbMATH — the first resource for mathematics

Reliable control for a class of uncertain singular systems with interval time-varying delay. (English) Zbl 1219.93105
Summary: This paper is concerned with the reliable controller design problem for a class of singular systems with interval time-varying delay and norm-bounded uncertainties. A more practical model of actuator failures than outages is considered. First, by constructing a novel Lyapunov-Krasovskii functional combined with Finsler’s Lemma, an improved delay-range-dependent stability criterion for the nominal unforced singular time-delay system is established in terms of linear matrix inequality. Then, based on this criterion, an LMI condition for the design of a reliable state feedback controller is presented such that, for all parameter uncertainties and actuator failures, the resultant closed-loop system is regular, impulse-free and stable. Numerical examples are proposed to illustrate the effectiveness of the proposed method.

MSC:
93D20 Asymptotic stability in control theory
93C15 Control/observation systems governed by ordinary differential equations
93B52 Feedback control
93C05 Linear systems in control theory
34H05 Control problems involving ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Hale, Introduction to Functional Differential Equations (1993) · Zbl 0787.34002
[2] Xu, Robust stability sand stabilization for singular systems with state delay and parameter uncertainty, IEEE Trans. Autom. Control 47 (7) pp 1122– (2002) · Zbl 1364.93723
[3] Fridman, H control of linear state-delay descriptor systems: an LMI approach, Linear Alg. Appl. 351-352 pp 271– (2002) · Zbl 1006.93021
[4] Su, Delay-dependent robust control for uncertain singular time-delay systems, Asian J. Control 8 (2) pp 1– (2006)
[5] Zhong, Delay-dependent robust control of descriptor systems with time delay, Asian J. Control 8 (1) pp 36– (2006)
[6] Du, Delay-dependent robust H control for uncertain singular systems with multiple state delays, IET Control Theory Appl. 3 (6) pp 731– (2009)
[7] Zhu, Delay-dependent robust stability criteria for two classes of uncertain singular time-delay systems, IEEE Trans. Autom. Control 52 (5) pp 880– (2007) · Zbl 1366.93478
[8] Wu, Delay-dependent robust H control for uncertain singular time-delay systems, IET Control Theory Appl. 1 (5) pp 1234– (2007)
[9] Xu, An improved characterization of bounded realness for singular delay systems and its applications, Int J. Robust Nonlinear Control 18 (3) pp 263– (2008) · Zbl 1284.93117
[10] Wu, Passivity-based sliding mode control of uncertain singular time-delay systems, Automatica 45 (9) pp 2120– (2009) · Zbl 1175.93065
[11] Wang, Absolute stability criteria for a class of nonlinear singular systems with time delay, Nonlinear Anal. Theory Methods Appl. 70 (2) pp 621– (2009) · Zbl 1168.34048
[12] Jiang , Z. W. Gui Y. Xie H. Wu Delay-dependent stabilization of singular linear continuous-time systems with time-varying state and input delays 1862 1867
[13] Wang , H. A. Xue R. Lu J. Wang Delay-dependent robust stability and stabilization for uncertain singular system with time-varying delay 1327 1331
[14] Lu, Delay-dependant robust stability and stabilization conditions for a class of Lur’e singular time-delay systems, Asian J. Control 10 (4) pp 462– (2008)
[15] Li, Observer-based resilient L2-L control for singular time-delay systems, IET Control Theory Appl. 3 (10) pp 1351– (2009)
[16] Kim, Delay-dependent robust and non-fragile guaranteed cost control for uncertain singular systems with time-varying state and input delays, Int. J. Control, Autom., Syst. 7 (3) pp 357– (2009)
[17] Gu, Further remarks on additional dynamics in various model transfor-mation of linear delay systems, IEEE Trans. Autom. Control 46 (3) pp 497– (2001) · Zbl 1056.93511
[18] He, Delay-range-dependent stability for systems with time-varying delay, Automatica 43 (2) pp 371– (2007) · Zbl 1111.93073
[19] Gao, A new delay system approach to network-based control, Automatica 44 (1) pp 39– (2008) · Zbl 1138.93375
[20] Liang, State estimation for coupled uncertain stochastic networks with missing measurements and time-varying delays: the discrete-time case, IEEE Trans. Neural Netw. 20 (5) pp 781– (2009)
[21] Wang, Robust H control for a class of nonlinear discrete time-delay stochastic systems with missing measurements, Automatica 45 (3) pp 684– (2009) · Zbl 1166.93319
[22] MacFarlane, Complex Variable Methods for Linear Multivariable Feedback Systems (1980)
[23] Yang, Reliable control of discrete-time systems with actuator failure, IEE Proc., Control Theory Appl. 147 (4) pp 428– (2000)
[24] Yu, An LMI approach to reliable guaranteed cost control of discrete-time systems with actuator failure, Appl. Math. Comput. 162 (3) pp 1325– (2005) · Zbl 1125.93046
[25] Ye, Reliable guaranteed cost control for linear state delayed systems with adaptive memory state feedback controllers, Asian J. Control 10 (6) pp 678– (2008)
[26] Yue, Reliable H control of uncertain descriptor systems with multiple time delays, IEE Proc., Control Theory Appl. 150 (6) pp 557– (2003)
[27] Dai, Singular Control Systems (1989) · Zbl 0669.93034
[28] de Souza, Robust H filtering for discrete-time linear systems with uncertain time-varying parameters, IEEE Trans. Signal Process. 54 (6) pp 2110– (2006) · Zbl 1373.93337
[29] Cao, Delay dependent robust H control for uncertain systems with time-varying delays, IEE Proc., Control Theory Appl. 145 (3) pp 338– (1998)
[30] Lam, Stability analysis for continuous systems with two additive time-varying delay components, Syst. Control Lett. 56 (1) pp 16– (2007) · Zbl 1120.93362
[31] Yue, A piecewise analysis method to stability analysis of linear continuous/discrete systems with time-varying delay, Int. J. Robust Nonlinear Control 19 (13) pp 1493– (2009) · Zbl 1298.93259
[32] Zhang, A delay decomposition approach to delay-dependent stability for linear systems with time-varying delays, Int. J. Robust Nonlinear Control 19 (17) pp 1922– (2009) · Zbl 1185.93106
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.