Stabilization for linear uncertain systems with switched time-varying delays

Abstract This paper is concerned with the robust stabilization problem for a class of uncertain linear time-delay systems with large delay periods. The aim of this paper is to design a state feedback controller such that the closed-loop system is exponentially stable and preserves a desired performance in the presence of large delays. In order to deal with the large delay periods, the original system is converted into a switched delay system, in which the delays are time-varying. The delay-dependent condition is established in terms of matrix inequalities. The desired controllers can be solved by the cone complementary linearization method. An example is presented to illustrate the effectiveness of the proposed technique.

[1]  Dong Yue,et al.  Delayed Feedback Guaranteed Cost Controller Design for Uncertain Time-Delay Systems , 2003, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[2]  Xinzhi Liu,et al.  Robust Stability Analysis of Guaranteed Cost Control for Impulsive Switched Systems , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[3]  Hiroaki Mukaidani,et al.  An LMI approach to guaranteed cost control for uncertain delay systems , 2003 .

[4]  Shengzhi Zhao,et al.  Nonlinear adaptive control for power integrator triangular systems by switching linear controllers , 2015 .

[5]  Kun Liu,et al.  Delay-dependent methods and the first delay interval , 2014, Syst. Control. Lett..

[6]  Guo-Ping Liu,et al.  Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays , 2004, Syst. Control. Lett..

[7]  T. K. C. Peng,et al.  Adaptive Guaranteed Cost of Control of Systems with Uncertain Parameters , 1970 .

[8]  L. Ghaoui,et al.  A cone complementarity linearization algorithm for static output-feedback and related problems , 1997, IEEE Trans. Autom. Control..

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

[10]  Ian R. Petersen,et al.  A riccati equation approach to the stabilization of uncertain linear systems , 1986, Autom..

[11]  M. Branicky.  Multiple Lyapunov functions and other analysis tools for switched and hybrid systems , 1998, IEEE Trans. Autom. Control..

[12]  Li Yu,et al.  An LMI approach to guaranteed cost control of linear uncertain time-delay systems , 1999, Autom..

[13]  Jun Fu,et al.  Global finite-time stabilization of a class of switched nonlinear systems with the powers of positive odd rational numbers , 2015, Autom..

[14]  Guo-Ping Liu,et al.  Delay-dependent stability for discrete systems with large delay sequence based on switching techniques , 2008, Autom..

[15]  Vladimir L. Kharitonov,et al.  Time-Delay Systems , 2013 .

[16]  Xun-lin Zhu,et al.  New stability criterion for linear switched systems with time‐varying delay , 2014 .

[17]  Jean-Pierre Richard,et al.  Time-delay systems: an overview of some recent advances and open problems , 2003, Autom..

[18]  Zhi-Gang Wu,et al.  Stabilization of switched delay systems with polytopic uncertainties under asynchronous switching , 2013, J. Frankl. Inst..

[19]  Shouming Zhong,et al.  Improved delay-dependent stability criteria for recurrent neural networks with time-varying delays , 2014, Neurocomputing.

[20]  Peng Shi,et al.  Design on H ∞-filtering for discrete-time switched delay systems , 2011, Int. J. Syst. Sci..

[21]  Jitao Sun,et al.  Consensus of discrete-time linear multi-agent systems with Markov switching topologies and time-delay , 2015, Neurocomputing.

[22]  U. Shaked,et al.  Stability and guaranteed cost control of uncertain discrete delay systems , 2005 .

[23]  Peng Shi,et al.  Input-to-State Stability for Nonlinear Systems With Large Delay Periods Based on Switching Techniques , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[24]  George Leitmann,et al.  Continuous feedback guaranteeing uniform ultimate boundedness for uncertain linear delay systems: An application to river pollution control , 1988 .

[25]  Ju H. Park.  Robust Stabilization for Dynamic Systems with Multiple Time-Varying Delays and Nonlinear Uncertainties , 2001 .

[26]  Tong Heng Lee,et al.  Adaptive robust control of uncertain time delay systems , 2005, Autom..

[27]  Bo Hu,et al.  Stability analysis of switched systems with stable and unstable subsystems: An average dwell time approach , 2001, Int. J. Syst. Sci..

[28]  Ju H. Park,et al.  On improved delay-dependent robust control for uncertain time-delay systems , 2004, IEEE Transactions on Automatic Control.

[29]  Shengyuan Xu,et al.  Delay-dependent guaranteed cost control for uncertain systems with state and input delays , 2006 .

[30]  Wei Zhang,et al.  Stability of networked control systems , 2001 .

[31]  Jun Zhao,et al.  Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings , 2010, Autom..