Finite-time stability of singular nonlinear switched time-delay systems: A singular value decomposition approach

Abstract In this paper, a constructive geometric design of switching laws is proposed for the finite-time stability of singular nonlinear switched systems subjected to delay and disturbance. The state-dependent switching law is constructed based on the construction of a partition of the stability state regions in convex cones such that each system mode is activated in one particular conic zone. Using the state-space singular value decomposition approach, new delay-dependent sufficient conditions for the finite-time stability of the system are presented in terms of linear matrix inequalities (LMIs). The obtained results are applied to uncertain linear singular switched systems with delay. Numerical examples are given to illustrate the effectiveness of the proposed method.

[1]  Yuanqing Xia,et al.  Stability and stabilization of continuous-time singular hybrid systems , 2009, Autom..

[2]  Jinxing Lin,et al.  Robust Exponential Admissibility of Uncertain Switched Singular Time-delay Systems , 2010 .

[3]  Arkadi Nemirovski,et al.  Lmi Control Toolbox For Use With Matlab , 2014 .

[4]  Lei Zhou,et al.  Stability analysis of switched linear singular systems , 2013, Autom..

[5]  F. Lewis.  A survey of linear singular systems , 1986 .

[6]  P. Dorato.  SHORT-TIME STABILITY IN LINEAR TIME-VARYING SYSTEMS , 1961 .

[7]  Asier Ibeas,et al.  Exponential stability of hybrid switched nonlinear singular systems with time-varying delay , 2013, J. Frankl. Inst..

[8]  Shengyuan Xu,et al.  Robust Control and Filtering of Singular Systems , 2006 .

[9]  Yantao Wang,et al.  Finite-time stability for singular linear time-delay systems with time-varying exogenous disturbance , 2013, CCDC 2013.

[10]  Yijing Wang,et al.  Average dwell time approach to finite-time stabilization of switched singular linear systems , 2015, J. Frankl. Inst..

[11]  Hamid Reza Karimi,et al.  On stability and stabilization of singular uncertain Takagi-Sugeno fuzzy systems , 2014, J. Frankl. Inst..

[12]  Guanghui Wen,et al.  H∞ control for uncertain switched nonlinear singular systems with time delay , 2013 .

[13]  Hui Zhang,et al.  Finite-time stability analysis and stabilization for uncertain continuous-time system with time-varying delay , 2015, J. Frankl. Inst..

[14]  L. Dai,et al.  Singular Control Systems , 1989, Lecture Notes in Control and Information Sciences.

[15]  F. Uhlig.  A recurring theorem about pairs of quadratic forms and extensions: a survey , 1979 .

[16]  Jun Huang,et al.  Absolute exponential stability of switched nonlinear time-delay systems , 2016, J. Frankl. Inst..

[17]  Yun Zou,et al.  Finite-time stability of switched nonlinear systems with finite-time unstable subsystems , 2015, J. Frankl. Inst..

[18]  G. Papavassilopoulos,et al.  A global optimization approach for the BMI problem , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[19]  S. Zhong,et al.  Finite-time filtering for switched linear systems with a mode-dependent average dwell time , 2015 .

[20]  Weijie Mao,et al.  Improved Stability and Stabilization Criteria of Singular System with Time-delay and Parameter Uncertainties ⋆ , 2013 .

[21]  Chuandong Li,et al.  Stability of switched neural networks with time delay , 2015 .

[22]  R. A. Smith,et al.  SINGULAR SYSTEMS OF DIFFERENTIAL EQUATIONS II: (Research Notes in Mathematics, 61) , 1983 .

[23]  Vu Ngoc Phat,et al.  Switched controller design for stabilization of nonlinear hybrid systems with time-varying delays in state and control , 2010, J. Frankl. Inst..

[24]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

[25]  P. Balasubramaniam,et al.  A descriptor system approach to the delay-dependent exponential stability analysis for switched neutral systems with nonlinear perturbations , 2015 .

[26]  S. Ge,et al.  Switched Linear Systems: Control and Design , 2005 .

[27]  Guisheng Zhai,et al.  Decentralized Hinfinity controller design: a matrix inequality approach using a homotopy method , 1998, Autom..

[28]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .