Stabilization of positive switched systems with time-varying delays under asynchronous switching

This paper investigates the state feedback stabilization problem for a class of positive switched systems with time-varying delays under asynchronous switching in the frameworks of continuous-time and discrete-time dynamics. The so-called asynchronous switching means that the switches between the candidate controllers and system modes are asynchronous. By constructing an appropriate co-positive type Lyapunov-Krasovskii functional and further allowing the functional to increase during the running time of active subsystems, sufficient conditions are provided to guarantee the exponential stability of the resulting closed-loop systems, and the corresponding controller gain matrices and admissible switching signals are presented. Finally, two illustrative examples are given to show the effectiveness of the proposed methods.

[1]  Zhengrong Xiang,et al.  Stability, L1-gain and control synthesis for positive switched systems with time-varying delay , 2013 .

[2]  Zhengrong Xiang,et al.  Robust control for uncertain switched non-linear systems with time delay under asynchronous switching , 2009 .

[3]  James Lam,et al.  ℓ1ℓ1-induced Norm and Controller Synthesis of Positive Systems , 2013, Autom..

[4]  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).

[5]  M. Mahmoud,et al.  Robust stability, stabilization and ℋ∞ control of time‐delay systems with Markovian jump parameters , 2003 .

[6]  H. Caswell.  Matrix population models : construction, analysis, and interpretation , 2001 .

[7]  Robert Shorten,et al.  On Linear Copositive Lyapunov Functions and the Stability of Switched Positive Linear Systems , 2007, IEEE Transactions on Automatic Control.

[8]  Gang Feng,et al.  Stabilisation of second-order LTI switched positive systems , 2011, Int. J. Control.

[9]  Huijun Gao,et al.  New Delay-Dependent Exponential H ∞ Synchronization for Uncertain Neural Networks With Mixed Time Delays , 2009 .

[10]  Xudong Zhao,et al.  Stability of a class of switched positive linear time‐delay systems , 2013 .

[11]  Gang Feng,et al.  Two slow stabilizing switching laws for discrete time positive switched systems , 2014 .

[12]  Long Wang,et al.  Stability Analysis of Positive Systems With Bounded Time-Varying Delays , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[13]  Jian Xiao,et al.  Asymptotic stability, ℓ2 gain, boundness analysis, and control synthesis for switched systems: a switching frequency approach , 2012 .

[14]  Federico Najson,et al.  State-feedback stabilizability, optimality, and convexity in switched positive linear systems , 2011, Proceedings of the 2011 American Control Conference.

[15]  Long Wang,et al.  Stabilization of switched linear systems with time-delay in detection of switching signal , 2005 .

[16]  Michael Margaliot,et al.  Nice reachability for planar bilinear control systems with applications to planar linear switched systems , 2009, IEEE Transactions on Automatic Control.

[17]  F. Tadeo,et al.  Control of constrained positive discrete systems , 2007, 2007 American Control Conference.

[18]  Zhengzhi Han,et al.  Robust stabilization of switched positive linear systems with uncertainties , 2013 .

[19]  Zhengrong Xiang,et al.  Robust reliable stabilization of uncertain switched neutral systems with delayed switching , 2011, Appl. Math. Comput..

[20]  L Finkelstein,et al.  Modeling and identification of metabolic systems. , 1981, The American journal of physiology.

[21]  ShortenRobert,et al.  A positive systems model of TCP-like congestion control , 2006 .

[22]  Zhi-Gang Wu,et al.  Dynamic output feedback control for a class of switched delay systems under asynchronous switching , 2013, Inf. Sci..

[23]  Tadeusz Kaczorek,et al.  The Choice of the Forms of Lyapunov Functions for a Positive 2D Roesser Model , 2007, Int. J. Appl. Math. Comput. Sci..

[24]  Zhengrong Xiang,et al.  Reliable L1 control of positive switched systems with time-varying delays , 2013 .

[25]  Peng Shi,et al.  Asynchronously switched control of a class of slowly switched linear systems , 2012, Syst. Control. Lett..

[26]  Chuangyin Dang,et al.  Stability Analysis of Positive Switched Linear Systems With Delays , 2011, IEEE Transactions on Automatic Control.

[27]  P. Shi,et al.  Exponential H∞ filtering for switched linear systems with interval time‐varying delay , 2009 .

[28]  Ettore Fornasini,et al.  Stability and stabilizability of special classes of discrete-time positive switched systems , 2011, ACC.

[29]  Fabian R. Wirth,et al.  A positive systems model of TCP-like congestion control: asymptotic results , 2006, IEEE/ACM Transactions on Networking.

[30]  Peng Shi,et al.  Stability and Stabilization of Switched Linear Systems With Mode-Dependent Average Dwell Time , 2012, IEEE Transactions on Automatic Control.

[31]  Jian Xiao,et al.  H ∞ filtering for switched nonlinear systems under asynchronous switching , 2011, Int. J. Syst. Sci..

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

[33]  Lou Caccetta,et al.  A positive linear discrete-time model of capacity planning and its controllability properties , 2004, Math. Comput. Model..

[34]  Magdi S. Mahmoud,et al.  Robust stability, stabilization and H-infinity control of time-delay systems with Markovian jump parameters , 2003 .

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

[36]  Jian Xiao,et al.  Stability analysis and control synthesis of switched impulsive systems , 2012 .

[37]  Hamid Reza Karimi,et al.  New Delay-Dependent Exponential $H_{\infty}$ Synchronization for Uncertain Neural Networks With Mixed Time Delays , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[38]  Peng Shi,et al.  Stability, ${l}_{2}$ -Gain and Asynchronous ${H}_{{\infty}}$ Control of Discrete-Time Switched Systems With Average Dwell Time , 2009, IEEE Transactions on Automatic Control.

[39]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[40]  Zhengzhi Han,et al.  Stability and stabilization of positive switched systems with mode-dependent average dwell time , 2013 .

[41]  Jian Xiao,et al.  Fault detection for switched nonlinear systems under asynchronous switching , 2011, Int. J. Control.

[42]  Peng Shi,et al.  Stability of switched positive linear systems with average dwell time switching , 2012, Autom..

[43]  Yan-Wu Wang,et al.  Stability analysis of switched positive linear systems with stable and unstable subsystems , 2014, Int. J. Syst. Sci..