Stability analysis for a class of switched nonlinear time-delay systems

This paper investigates the stability analysis for a class of discrete-time switched nonlinear time-delay systems. These systems are modelled by a set of delay difference equations, which are represented in the state form. Then, another transformation is made towards an arrow form. Therefore, by applying the Kotelyanski conditions combined to the M−matrix properties, new delay-independent sufficient stability conditions under arbitrary switching which correspond to a Lyapunov function vector are established. The obtained results are explicit and easy to use. A numerical example is provided to show the effectiveness of the developed results.

[1]  F. Robert.  Recherche d'uneM-matrice parmi les minorantes d'un opérateur linéaire , 1966 .

[2]  F. Gantmakher,et al.  Théorie des matrices , 1990 .

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

[4]  A. Morse,et al.  Basic problems in stability and design of switched systems , 1999 .

[5]  A. Morse,et al.  Stability of switched systems with average dwell-time , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[6]  Hyungbo Shim,et al.  Common Lyapunov Function for Exponentially Stable Nonlinear Systems , 2001 .

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

[8]  Chi K. Tse,et al.  Complex behavior in switching power converters , 2002, Proc. IEEE.

[9]  Bruce A. Francis,et al.  Stabilizing a linear system by switching control with dwell time , 2002, IEEE Trans. Autom. Control..

[10]  Pierre Apkarian,et al.  MISSILE AUTOPILOT DESIGN VIA A MULTI-CHANNEL LFT/LPV CONTROL METHOD , 2002 .

[11]  Shengyuan Xu.  Robust H/sub /spl infin// filtering for a class of discrete-time uncertain nonlinear systems with state delay , 2002 .

[12]  Shengyuan Xu,et al.  Robust Filtering for a Class of Discrete-Time Uncertain Nonlinear Systems with State Delay , 2002 .

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

[14]  Daniel Liberzon,et al.  Nonlinear Systems , 2004 .

[15]  Mohamed Benrejeb,et al.  New Discrete Tanaka Sugeno Kang Fuzzy Systems Characterization and Stability Domain , 2006, Int. J. Comput. Commun. Control.

[16]  Zidong Wang,et al.  Discrete bilinear stochastic systems with time-varying delay: Stability analysis and control synthesis , 2007 .

[17]  Huijun Gao,et al.  New Results on Stability of Discrete-Time Systems With Time-Varying State Delay , 2007, IEEE Transactions on Automatic Control.

[18]  P. Shi,et al.  Robust stability and stabilisation of uncertain switched linear discrete time-delay systems , 2008 .

[19]  Wei Wang,et al.  Stability Analysis for Linear Switched Systems With Time-Varying Delay , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[20]  Wen-an Zhang,et al.  Stability analysis for discrete-time switched time-delay systems , 2009, Autom..

[21]  Jianghai Hu,et al.  Exponential stabilization of discrete-time switched linear systems , 2009, Autom..

[22]  Magdi S. Mahmoud,et al.  Switched Time-Delay Systems , 2010 .

[23]  Kai Liu,et al.  Stabilization of nonlinear systems under arbitrary switching law , 2010, Proceedings of the 29th Chinese Control Conference.

[24]  Huijun Gao,et al.  Asynchronously switched control of switched linear systems with average dwell time , 2010, Autom..

[25]  Huaguang Zhang,et al.  Novel Delay-Dependent Robust Stability Analysis for Switched Neutral-Type Neural Networks With Time-Varying Delays via SC Technique , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[26]  V. Phat,et al.  Stability and stabilization of switched linear discrete-time systems with interval time-varying delay , 2011 .

[27]  C. Lien,et al.  Switching signal design for global exponential stability of uncertain switched nonlinear systems with time-varying delay , 2011 .

[28]  École Nationale.  New delay-dependent stability conditions for linear systems with delay , 2011 .

[29]  Peng Shi,et al.  Delay-Dependent Stability Analysis for Switched Neural Networks With Time-Varying Delay , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[30]  M. Benrejeb,et al.  New delay-dependent stability conditions for linear systems with delay , 2011, 2011 International Conference on Communications, Computing and Control Applications (CCCA).

[31]  S. Mei,et al.  Stabilization for switched nonlinear time-delay systems , 2011 .

[32]  Anis Sakly,et al.  A New Stability Analysis and Stabilization Of Discrete-Time Switched Linear Systems Using Vector Norms Approach , 2012 .

[33]  Rathinasamy Sakthivel,et al.  New robust exponential stability results for discrete-time switched fuzzy neural networks with time delays , 2012, Comput. Math. Appl..

[34]  Mohamed Benrejeb,et al.  On Synchronization, Anti-synchronization and Hybrid Synchronization of 3D Discrete Generalized H enon Map , 2012 .

[35]  Rathinasamy Sakthivel,et al.  Robust stability criteria for discrete-time switched neural networks with various activation functions , 2012, Appl. Math. Comput..

[36]  Long-Yeu Chung,et al.  Switching signal design for exponential stability of discrete switched systems with interval time-varying delay , 2012, J. Frankl. Inst..

[37]  Mohamed Benrejeb,et al.  On stability analysis of nonlinear discrete singularly perturbed T-S fuzzy models , 2013 .

[38]  Rathinasamy Sakthivel,et al.  State estimation for switched discrete-time stochastic BAM neural networks with time varying delay , 2013 .

[39]  Anis Sakly,et al.  A New Stability Analysis for Discrete-Time Switched Time-Delay Systems , 2013 .

[40]  M. Darouach,et al.  Admissibility and control of switched discrete-time singular systems , 2013 .

[41]  Karolin Papst,et al.  Stability Theory Of Switched Dynamical Systems , 2016 .