Exponential stability of switched positive systems with unstable modes and distributed delays

Abstract This paper studies the exponential stability of switched positive system consisting of unstable subsystems with distributed time-varying delay. Unlike the existing results concerning delays, switching behaviors dominating the system can be either stabilizing or destabilizing. The distributed delay is supposed to be slowly varying and upper-bounded. To tackle the difficulties brought by both the switching behaviors with mixed effects and the distributed delay, a multiple discretized Lyapunov-Krasovskii functional is employed to derive sufficient conditions for the exponential stability of the system. Specifically, by adjusting the ratio of the stabilizing switching behaviors, the state divergence caused by unstable subsystems and destabilizing switching behaviors can be compensated. Simulation examples demonstrate the effectiveness of the results.

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

[2]  Jie Lian,et al.  Stabilization of Switched Linear Systems Subject to Actuator Saturation via Invariant Semiellipsoids , 2020, IEEE Transactions on Automatic Control.

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

[4]  Zhengrong Xiang,et al.  Finite-time L1 control for positive switched linear systems with time-varying delay , 2013, Commun. Nonlinear Sci. Numer. Simul..

[5]  Hamid Reza Karimi,et al.  Stability and L1-gain controller design for positive switched systems with mixed time-varying delays , 2013 .

[6]  Hongchao Li,et al.  Exponential Stabilization for Networked Switched Positive Systems with Mixed Time-Varying Delays via an Event-Triggered Scheme , 2020, 2020 Chinese Control And Decision Conference (CCDC).

[7]  F. Tadeo,et al.  Positive observation problem for linear time-delay positive systems , 2007, 2007 Mediterranean Conference on Control & Automation.

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

[9]  Y. M. Ram,et al.  Stability boundaries of mechanical controlled system with time delay , 2012 .

[10]  Xudong Zhao,et al.  Stability of switched positive linear time‐delay systems , 2019, IET Control Theory & Applications.

[11]  Oliver Mason,et al.  On Diagonal Stability of Positive Systems with Switches and Delays , 2018, Autom. Remote. Control..

[12]  Jian Xiao,et al.  Stabilization of switched continuous-time systems with all modes unstable via dwell time switching , 2014, Autom..

[13]  Mohamed Chaabane,et al.  Exponential Stability Criteria for Positive Systems with Time-Varying Delay: A Delay Decomposition Technique , 2016, Circuits Syst. Signal Process..

[14]  Lan Wang,et al.  Switched mechanisms for stability and l1-gain analysis of T-S fuzzy positive systems described by the F-M second model , 2018, J. Frankl. Inst..

[15]  Hamid Reza Karimi,et al.  Conditions for the Stability of Switched Systems Containing Unstable Subsystems , 2019, IEEE Transactions on Circuits and Systems II: Express Briefs.

[16]  Zhengrong Xiang,et al.  Stability and $${L_{\infty }}$$L∞-Gain Analysis for Positive Switched Systems with Time-Varying Delay Under State-Dependent Switching , 2016, Circuits Syst. Signal Process..

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

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

[19]  Tingwen Huang,et al.  l1 filtering for continuous-discrete T-S fuzzy positive Roesser model , 2018, J. Frankl. Inst..

[20]  Jie Lian,et al.  Fuzzy Control of Uncertain Positive Markov Jump Fuzzy Systems With Input Constraint , 2019, IEEE Transactions on Cybernetics.

[21]  Dirk Aeyels,et al.  Stabilization of positive linear systems , 2001, Syst. Control. Lett..

[22]  Jin-Hoon Kim,et al.  Note on stability of linear systems with time-varying delay , 2011, Autom..

[23]  Yonggui Kao,et al.  Stability and Stabilization for Singular Switching Semi-Markovian Jump Systems With Generally Uncertain Transition Rates , 2018, IEEE Transactions on Automatic Control.

[24]  Jie Lian,et al.  Output feedback L1 finite-time control of switched positive delayed systems with MDADT , 2015 .

[25]  Meng Liu,et al.  Brief Paper - Exponential stability of impulsive positive systems with mixed time-varying delays , 2014 .

[26]  Jun Zhao,et al.  Stability and robust stability of switched positive linear systems with all modes unstable , 2019, IEEE/CAA Journal of Automatica Sinica.

[27]  Jianwei Xia,et al.  Reachable set estimation for switched positive systems with mixed time‐varying delays and bounded disturbances , 2018, IET Control Theory & Applications.

[28]  Zheng Yan,et al.  Exponential stability of linear switched positive systems with distributed delays , 2015, 2015 34th Chinese Control Conference (CCC).

[29]  Cuihong Wang,et al.  Stability and L∞ performance analysis of positive systems with bounded time-varying delays on time scales , 2020 .

[30]  Fernando Tadeo,et al.  State-feedback with memory for controlled positivity with application to congestion control , 2010 .

[31]  Hamid Reza Karimi,et al.  Takagi–Sugeno Model Based Event-Triggered Fuzzy Sliding-Mode Control of Networked Control Systems With Semi-Markovian Switchings , 2020, IEEE Transactions on Fuzzy Systems.

[32]  Wassim M. Haddad,et al.  Stability theory for nonnegative and compartmental dynamical systems with time delay , 2004, Proceedings of the 2004 American Control Conference.

[33]  Long Wang,et al.  Stability Analysis for Continuous-Time Positive Systems With Time-Varying Delays , 2010, IEEE Transactions on Automatic Control.

[34]  Wu Yang,et al.  Exponential stability of switched positive systems with all modes being unstable , 2020, International Journal of Robust and Nonlinear Control.

[35]  Xianfu Zhang,et al.  Stabilization of positive switched delay systems with all modes unstable , 2018, Nonlinear Analysis: Hybrid Systems.