×
Li, Fanbiao; Zhang, Xian

A delay-dependent bounded real lemma for singular LPV systems with time-variant delay. (English) Zbl 1273.93088

Int. J. Robust Nonlinear Control 22, No. 5, 559-574 (2012); corrigendum ibid. 23, No. 5, 590 (2013).
Summary: This paper is concerned with establishing a delay-dependent Bounded Real Lemma (BRL) for singular Linear Parameter-Varying (LPV) systems with time-variant delay. In terms of linear matrix inequality, a delay-dependent BRL is presented to ensure singular time-delay LPV systems to be admissible and satisfy a prescribed \(H_{\infty }\) performance level. The BRL is obtained based on the construction of a parameter-dependent Lyapunov-Krasovskii functional. The effectiveness of the proposed approach is shown by several numerical examples.

Cited in 1 Review
Cited in 36 Documents

MSC:

93C15 Control/observation systems governed by ordinary differential equations
93C05 Linear systems in control theory
93B36 \(H^\infty\)-control
93D99 Stability of control systems

Keywords:

singular linear parameter-varying (LPV) systems; time-variant delay; bounded real lemma; stability
PDF BibTeX XML Cite
\textit{F. Li} and \textit{X. Zhang}, Int. J. Robust Nonlinear Control 22, No. 5, 559--574 (2012; Zbl 1273.93088)
Full Text: DOI

References:

[1] Hale, Theory of Functional Differential Equations (1977) · Zbl 0352.34001
[2] Kuang, Delay Differential Equations: with Applications in Population Dynamics (1993) · Zbl 0777.34002
[3] Gao HL Zhu SQ Cheng ZL Xu BG Delay-dependent state feedback guaranteed cost control uncertain singular time-delay systems 4354 4359
[4] Wang HJ Xue AK Lu RQ Wang JH Delay-dependent robust stability and stabilization for uncertain singular system with time-varying delay 3626 3631
[5] Gao JF Lei MZ Pan HP New delay-dependent criteria for stability and stabilization of uncertain singular systems with time delay 703 708
[6] Zhu SQ Cheng ZL Feng J Delay-dependent robust stability criterion and robust stabilization for uncertain singular time-delay systems 2839 2844
[7] Zhu XL Yang GH New results of stability analysis for singular time-delay systems 4904 4908
[8] Sun, An improved approach to delay-dependent robust stabilization for uncertain singular time-delay systems, International Journal of Automation and Computing 7 (2) pp 205– (2010)
[9] Xu, Robust H control for uncertain singular systems with state delay, International Journal of Robust and Nonlinear Control 13 pp 1213– (2003) · Zbl 1039.93019
[10] Wu, Delay-dependent robust H control for uncertain singular time-delay systems, IET Control Theory and Applications 1 pp 1234– (2007)
[11] Fridman, H-control of linear state-delay descriptor systems: an LMI approach, Linear Algebra and its Applications 351-352 pp 271– (2002) · Zbl 1006.93021
[12] Yang, Delay-dependent H control for linear descriptor systems with delay in state, Journal of Control Theory and Applications (English Series) 3 (1) pp 76– (2005)
[13] Zhong, Delay-dependent robust control of descriptor systems with time delay, Asian Journal of Control 8 (1) pp 36– (2006)
[14] Wu, Improved results on delay-dependent H control for singular time-delay systems, Acta Automatica Sinica 35 (8) pp 1101– (2009) · Zbl 1212.93088
[15] Xu, An improved characterization of bounded realness for singular delay systems and its applications, International Journal of Robust and Nonlinear Control 18 pp 263– (2008) · Zbl 1284.93117
[16] Du, Delay-dependent robust H control for uncertain singular systems with multiple state delays, IET Control Theory and Applications 3 (6) pp 731– (2009)
[17] Yang, Robust non-fragile H control for a class of uncertain singular systems with multiple time-delays, International Journal of Information and Systems Science 5 (2) pp 488– (2009)
[18] Wang, Gain-scheduled guaranteed cost control of LPV systems with time-varying state and input delays, International Journal of Innovative Computing Information and Control 5 (10B) pp 3377– (2009)
[19] Briat, Delay-scheduled state-feedback design for time-delay systems with time-varying delays-a LPV approach, Systems and Control Letters 58 (9) pp 664– (2009) · Zbl 1184.93058
[20] Lu, Switching LPV control of an F-16 aircraft via controller state reset, IEEE Transactions on Control Systems Technology 14 (2) pp 267– (2006)
[21] He, Robust LPV control of diesel auxiliary power unit for series hybrid electric vehicles, IEEE Transactions on Power Electronics 21 (3) pp 791– (2006)
[22] Qin, Modeling and control design for performance management of Web servers via an LPV approach, IEEE Transactions on Control Systems Technology 15 (2) pp 259– (2007)
[23] Gao XY Duan GR Zhang X Parameter-dependent Lyapunov function approach to robust stability analysis for discrete-time descriptor polytopic systems 1139 1144
[24] Li FB Zhang X Stability analysis of singular LPV systems with time-varying delays: a projection approach 944 949
[25] Briat C Sename O Lafay J H filtering of uncertain LPV systems with time-delays · Zbl 1198.93087
[26] Briat C Robust control and observation of LPV time-delay systems 2008
[27] Han, Absolute stability of time-delay systems with sector-bounded nonlinearity, Automatica 41 pp 2171– (2005) · Zbl 1100.93519
[28] Gouaisbaut F Peaucelle D Delay dependent robust stability of time delay-systems · Zbl 1293.93589
[29] Dai, Lecture Notes on Control and Information Sciences, in: Singular Control Systems (1989)
[30] Gahinet, Affine parameter-dependent Lyapunov functions and real parametric uncertainty, IEEE Transactions on Automatic Control 41 (3) pp 436– (1996) · Zbl 0854.93113
[31] de Oliveira, Perspectives in Robust Control Reza (2001)
[32] Gu K An integral inequality in the stability problem of time-delay systems 2805 2810
[33] Xu, Robust stability and stabilization for singular systems with state delay and parameter uncertainty, IEEE Transactions on Automatic Control 47 (7) pp 1122– (2002) · Zbl 1364.93723
[34] Haidar, Exponential stability and static output feedback stabilisation of singular time-delay systems with saturating actuators, IET Control Theory and Applications 3 (9) pp 1293– (2009)
[35] Zhu, Delay-dependent robust stability criteria for two classes of uncertain singular time-delay systems, IEEE Transactions on Automatic Control 52 (2) pp 880– (2007) · Zbl 1366.93478
[36] Yue, A delay-dependent stability criterion of neutral systems and its application to a partial element equivalent circuit model, IEEE Transactions on Circuits and Systems 51 (12) pp 685– (2004)
[37] Fridman, Stability of linear descriptor systems with delay: a Lyapunov-based approach, Journal of Mathematical Analysis and Applications 273 (1) pp 24– (2002) · Zbl 1032.34069
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.