Brief paper: new result on exponential stability for singular systems with two interval time-varying delays

This article mainly studies the problem of the exponential stability for singular systems with two interval time-varying delays. By constructing a modified Lyapunov-Krasovskii functional (LKF) and utilising a convex polyhedron method to estimate the derivative of LKF, some new delay-dependent criteria can be established in terms of linear matrix inequalities. Compared with some existing literatures, the novelties in this study are that the needed decisive variables are fewer and the obtained delay-dependent stability criteria are less conservative. Finally, two illustrative numerical examples are given to show the effectiveness of the derived results.

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

[2]  Peng Shi,et al.  Delay-dependent stability analysis for discrete-time singular Markovian jump systems with time-varying delay , 2012, Int. J. Syst. Sci..

[3]  Chenghui Zhang,et al.  Delay decomposition approach to delay-dependent stability for singular time-delay systems [Brief Paper] , 2010 .

[4]  J. Lam,et al.  An improved characterization of bounded realness for singular delay systems and its applications , 2008 .

[5]  PooGyeon Park,et al.  Stability and robust stability for systems with a time-varying delay , 2007, Autom..

[6]  Jian Sun,et al.  Improved stability criteria for linear systems with time-varying delay , 2010 .

[7]  Zhaolin Cheng,et al.  Delay-Dependent Robust Stability Criteria for Two Classes of Uncertain Singular Time-Delay Systems , 2007, IEEE Transactions on Automatic Control.

[8]  Qing-Long Han,et al.  Delay-dependent robust stability for uncertain linear systems with interval time-varying delay , 2006, Autom..

[9]  Huijun Gao,et al.  State Estimation and Sliding-Mode Control of Markovian Jump Singular Systems , 2010, IEEE Transactions on Automatic Control.

[10]  Ting Wang,et al.  Delay-Derivative-Dependent Stability for Delayed Neural Networks With Unbound Distributed Delay , 2010, IEEE Transactions on Neural Networks.

[11]  Yeong-Jeu Sun,et al.  Stability criterion for a class of descriptor systems with discrete and distributed time delays , 2007 .

[12]  Shengyuan Xu,et al.  Robust stability and stabilization for singular systems with state delay and parameter uncertainty , 2002, IEEE Trans. Autom. Control..

[13]  W. Greub.  Linear Algebra , 1981 .

[14]  James Lam,et al.  Exponential estimates and stabilization of uncertain singular systems with discrete and distributed delays , 2008, Int. J. Control.

[15]  Dong Yue,et al.  An improvement on "Delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty" , 2002, IEEE Trans. Autom. Control..

[16]  S. Ma,et al.  Delay-dependent robust H∞ control for uncertain discrete-time singular systems with time-delays , 2008 .

[17]  Jinxing Lin,et al.  New delay-range-dependent exponential estimates for singular systems with time-varying delay , 2011 .

[18]  Ahmad Haidar,et al.  Exponential stability of singular systems with multiple time-varying delays , 2009, Autom..

[19]  C. D. Souza,et al.  Delay-dependent robust stability and stabilization of uncertain linear delay systems: a linear matrix inequality approach , 1997, IEEE Trans. Autom. Control..

[20]  E. Fridman.  Stability of linear descriptor systems with delay: a Lyapunov-based approach , 2002 .

[21]  Shengyuan Xu,et al.  Improved delay-dependent stability criteria for time-delay systems , 2005, IEEE Transactions on Automatic Control.

[22]  Dong Yue,et al.  Delay-Distribution-Dependent Stability and Stabilization of T–S Fuzzy Systems With Probabilistic Interval Delay , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[23]  James Lam,et al.  Further Results on Exponential Estimates of Markovian Jump Systems With Mode-Dependent Time-Varying Delays , 2011, IEEE Transactions on Automatic Control.

[24]  Jian-Ning Li,et al.  Less conservative robust stability criteria for uncertain discrete stochastic singular systems with time-varying delay , 2013, Int. J. Syst. Sci..

[25]  Renquan Lu,et al.  Delay-dependant robust stability and stabilization conditions for a class of Lur'e singular time-delay systems† , 2008 .

[26]  Daniel W. C. Ho,et al.  Sliding mode control of singular stochastic hybrid systems , 2010, Autom..

[27]  S. Ma,et al.  Delay-dependent robust stability and stabilisation for uncertain discrete singular systems with time-varying delays , 2007 .

[28]  Hanyong Shao,et al.  New delay-dependent stability criteria for systems with interval delay , 2009, Autom..

[29]  Hamid Reza Karimi,et al.  Robust mixed H2/H∞ delayed state feedback control of uncertain neutral systems with time‐varying delays , 2008 .

[30]  Qing-Guo Wang,et al.  Delay-range-dependent stability for systems with time-varying delay , 2007, Autom..

[31]  Guo-Ping Liu,et al.  Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties , 2004, IEEE Transactions on Automatic Control.

[32]  Yong He,et al.  Delay-dependent criteria for robust stability of time-varying delay systems , 2004, Autom..

[33]  Thongchai Botmart,et al.  Delay-dependent exponential stabilization for uncertain linear systems with interval non-differentiable time-varying delays , 2011, Appl. Math. Comput..

[34]  Lihua Xie,et al.  Further Improvement of Free-Weighting Matrices Technique for Systems With Time-Varying Delay , 2007, IEEE Transactions on Automatic Control.

[35]  Dan Zhang,et al.  Exponential H∞ filtering for discrete-time switched singular systems with time-varying delays , 2012, J. Frankl. Inst..

[36]  Ligang Wu,et al.  Sliding mode control with bounded L2 gain performance of Markovian jump singular time-delay systems , 2012, Autom..

[37]  Qingling Zhang,et al.  New delay‐dependent robust stability of discrete singular systems with time‐varying delay , 2011 .

[38]  Jin-Hoon Kim,et al.  Delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty , 2001, IEEE Trans. Autom. Control..

[39]  Wei Xing Zheng,et al.  Passivity-based sliding mode control of uncertain singular time-delay systems , 2009, Autom..

[40]  Min Meng,et al.  Exponential stability for positive systems with bounded time-varying delays and static output feedback stabilization , 2013, J. Frankl. Inst..

[41]  E. Boukas,et al.  Exponential stability and static output feedback stabilisation of singular time-delay systems with saturating actuators , 2009 .

[42]  M. Benrejeb,et al.  Exponential stability and stabilization of linear systems with time varying delays , 2009, 2009 6th International Multi-Conference on Systems, Signals and Devices.

[43]  Shengyuan Xu,et al.  On Stability and Stabilizability of Singular Stochastic Systems with Delays , 2005 .

[44]  Dong Yue,et al.  Robust H/sub /spl infin// filter design of uncertain descriptor systems with discrete and distributed delays , 2004, IEEE Transactions on Signal Processing.

[45]  Q.-L. Han,et al.  Delay-dependent robust H∞ controller design for uncertain descriptor systems with time-varying discrete and distributed delays , 2005 .

[46]  Yeong-Jeu Sun.  Exponential stability for continuous-time singular systems with multiple time delays , 2003 .

[47]  Shen Cong,et al.  On Exponential Stability Conditions of Descriptor Systems with Time-Varying Delay , 2012, J. Appl. Math..

[48]  El-Kébir Boukas,et al.  Control of Singular Systems with Random Abrupt Changes , 2008 .

[49]  E. Fridman,et al.  H∞-control of linear state-delay descriptor systems: an LMI approach , 2002 .