Dissipativity of positive switched systems using multiple linear supply rates

Abstract In this paper, we are devoted to investigating dissipativity for a class of positive switched systems by exploiting multiple linear copositive storage functions and multiple linear supply rates. A novel concept of dissipativity is presented, which depicts the overall dissipativity property of positive switched systems without the requirement of the classic dissipativity property of each positive subsystem. A sufficient condition ensuring dissipativity for positive switched systems is given under a designed switching signal. Meanwhile, L 1 gain and stability are also get based on dissipativity. Dissipativity and positivity are shown to be maintained under positive feedback interconnection, and a small-gain property is also given. All presented conditions are formulated as a linear programming problem. Two examples are provided to illustrate the effectiveness of the main results.

[1]  Jun Zhao,et al.  Dissipativity Theory for Switched Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[2]  Lijun Long,et al.  Multiple Lyapunov Functions-Based Small-Gain Theorems for Switched Interconnected Nonlinear Systems , 2017, IEEE Transactions on Automatic Control.

[3]  Peng Shi,et al.  Passivity and Passification for a Class of Uncertain Switched Stochastic Time-Delay Systems , 2013, IEEE Transactions on Cybernetics.

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

[5]  David J. Hill,et al.  Decomposable Dissipativity and Related Stability for Discrete-Time Switched Systems , 2011, IEEE Transactions on Automatic Control.

[6]  Corentin Briat,et al.  Robust stability and stabilization of uncertain linear positive systems via Integral Linear Constraints: L1- and Linfinity-gains characterization , 2012, ArXiv.

[7]  Franco Blanchini,et al.  Co-Positive Lyapunov Functions for the Stabilization of Positive Switched Systems , 2012, IEEE Transactions on Automatic Control.

[8]  Jun Zhao,et al.  On stability, L2-gain and Hinfinity control for switched systems , 2008, Autom..

[9]  Corentin Briat,et al.  Stability and performance analysis of linear positive systems with delays using input–output methods , 2017, Int. J. Control.

[10]  Bin Jiang,et al.  Fault Tolerance Analysis for Switched Systems Via Global Passivity , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[11]  Shuzhi Sam Ge,et al.  Analysis and synthesis of switched linear control systems , 2005, Autom..

[12]  Wei Xing Zheng,et al.  State Estimation of Discrete-Time Switched Neural Networks With Multiple Communication Channels , 2017, IEEE Transactions on Cybernetics.

[13]  W. Haddad,et al.  Stability and dissipativity theory for nonnegative dynamical systems: a unified analysis framework for biological and physiological systems , 2005 .

[14]  F. Tadeo,et al.  Controller Synthesis for Positive Linear Systems With Bounded Controls , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[15]  Z. Xiang,et al.  Robust fault detection for switched positive linear systems with time-varying delays. , 2014, ISA transactions.

[16]  Jun Zhao,et al.  Stabilisation of switched positive systems with actuator saturation , 2016 .

[17]  Dong Yang,et al.  Dissipativity for Switched LPV Systems and Its Application: A Parameter and Dwell Time-Dependent Multiple Storage Functions Method , 2020, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[18]  Xunyuan Yin,et al.  Resilient Estimation for Networked Systems With Variable Communication Capability , 2016, IEEE Transactions on Automatic Control.

[19]  J. Willems.  Dissipative dynamical systems Part II: Linear systems with quadratic supply rates , 1972 .

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

[21]  Dimitri Peaucelle,et al.  L1 gain analysis of linear positive systems and its application , 2011, IEEE Conference on Decision and Control and European Control Conference.

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

[23]  Fen Wu,et al.  Switching LPV control designs using multiple parameter-dependent Lyapunov functions , 2004, Autom..

[24]  Fen Wu,et al.  Switching LPV control of an F-16 aircraft via controller state reset , 2006, IEEE Trans. Control. Syst. Technol..

[25]  Franco Blanchini,et al.  Discrete‐time control for switched positive systems with application to mitigating viral escape , 2011 .

[26]  Jun Zhao,et al.  Dissipativity and feedback passivation for switched discrete-time nonlinear systems , 2016, Syst. Control. Lett..

[27]  Hamid Reza Karimi,et al.  Adaptive Output-Feedback Controller Design for Switched Nonlinear Stochastic Systems With a Modified Average Dwell-Time Method , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[28]  Wassim M. Haddad,et al.  Dissipativity theory for nonnegative and compartmental dynamical systems with time delay , 2004, IEEE Transactions on Automatic Control.

[29]  Donghua Zhou,et al.  A Descriptor System Approach to Stability and Stabilization of Discrete-Time Switched PWA Systems , 2018, IEEE Transactions on Automatic Control.

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

[31]  Jian Xiao,et al.  Dissipativity and dwell time specifications of switched discrete-time systems and its applications in H∞ and robust passive control , 2015, Inf. Sci..

[32]  Panos J. Antsaklis,et al.  Stability of interconnected switched systems using QSR dissipativity with multiple supply rates , 2012, 2012 American Control Conference (ACC).

[33]  James Lam,et al.  Static output-feedback stabilization with optimal L1-gain for positive linear systems , 2016, Autom..

[34]  Xi-Ming Sun,et al.  Stability of switched nonlinear systems with delay and disturbance , 2016, Autom..

[35]  Patrizio Colaneri,et al.  Passivity of switched linear systems: Analysis and control design , 2012, Syst. Control. Lett..

[36]  Tianyou Chai,et al.  Dwell-Time-Based Observer Design for Unknown Input Switched Linear Systems Without Requiring Strong Detectability of Subsystems , 2017, IEEE Transactions on Automatic Control.

[37]  Zhengzhi Han,et al.  L1-gain analysis and control synthesis of positive switched systems , 2015, Int. J. Syst. Sci..

[38]  Changhong Wang,et al.  Stabilisation of discrete-time switched positive linear systems via time- and state-dependent switching laws , 2012 .

[39]  Weiming Xiang,et al.  Robust Exponential Stability and Disturbance Attenuation for Discrete-Time Switched Systems Under Arbitrary Switching , 2018, IEEE Transactions on Automatic Control.

[40]  S. Rinaldi,et al.  Positive Linear Systems: Theory and Applications , 2000 .

[41]  Hai Lin,et al.  Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results , 2009, IEEE Transactions on Automatic Control.

[42]  Hanz Richter,et al.  Advanced Control of Turbofan Engines , 2011 .

[43]  Hai Lin,et al.  On l1 stability of switched positive singular systems with time‐varying delay , 2017 .