Absolute exponential L1-gain analysis and synthesis of switched nonlinear positive systems with time-varying delay

This paper investigates absolute exponential stability and stabilization with L1-gain performance of switched nonlinear positive systems with time-varying delay. Nonlinear functions considered in the paper are located in a sector field and the time-varying delay is unknown but bounded. The notion of absolute exponential L1 stability of switched nonlinear positive systems is first introduced. A nonlinear Lyapunov-Krasovskii functional is constructed for the underlying systems. By using the Lyapunov-Krasovskii functional, a sufficient condition for absolute exponential L1 stability of the systems is established in terms of linear programming. Then, absolute exponential L1 control synthesis of the systems is addressed. A feedback control law containing nonlinear functions and a state-feedback control law are designed, respectively. By comparing with existing results, it is shown that the present design is less conservative. Finally, an illustrative example is provided to illustrate the effectiveness of the results.

[1]  Jun Huang,et al.  Brief paper: feedback control for switched positive linear systems , 2013 .

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

[3]  Michael Margaliot,et al.  On the Stability of Positive Linear Switched Systems Under Arbitrary Switching Laws , 2009, IEEE Transactions on Automatic Control.

[4]  Shihua Li,et al.  Finite-time boundedness and L2-gain analysis for switched delay systems with norm-bounded disturbance , 2011, Appl. Math. Comput..

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

[6]  Stuart Townley,et al.  Positive state controllability of positive linear systems , 2014, Syst. Control. Lett..

[7]  Jun Zhao,et al.  Global output-feedback stabilization for a class of switched uncertain nonlinear systems , 2015, Appl. Math. Comput..

[8]  James Lam,et al.  L∞-gain analysis for positive systems with distributed delays , 2014, Autom..

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

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

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

[12]  Yuxin Zhao,et al.  Reduced-order fuzzy modeling for nonlinear switched systems , 2014, 53rd IEEE Conference on Decision and Control.

[13]  Hamid Reza Feyzmahdavian,et al.  Exponential Stability of Homogeneous Positive Systems of Degree One With Time-Varying Delays , 2013, IEEE Transactions on Automatic Control.

[14]  Cédric Langbort,et al.  A linear programming approach to routing control in networks of constrained linear positive systems , 2012, Autom..

[15]  F. Fairman.  Introduction to dynamic systems: Theory, models and applications , 1979, Proceedings of the IEEE.

[16]  Jian Xiao,et al.  Robust fault detection for a class of uncertain switched nonlinear systems via the state updating approach , 2014 .

[17]  Bart De Schutter,et al.  Stabilization and robust H⃵ control for sector-bounded switched nonlinear systems , 2014, Autom..

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

[19]  Weihai Zhang,et al.  Finite-Time Stability and Stabilization of Itô Stochastic Systems With Markovian Switching: Mode-Dependent Parameter Approach , 2015, IEEE Transactions on Automatic Control.

[20]  Long Wang,et al.  On stability of a class of switched nonlinear systems , 2013, Autom..

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

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

[23]  Zhengrong Xiang,et al.  Exponential stability of discrete-time switched linear positive systems with time-delay , 2014, Appl. Math. Comput..

[24]  J. Geromel,et al.  Dwell time analysis for continuous-time switched linear positive systems , 2010, Proceedings of the 2010 American Control Conference.

[25]  Guoshan Zhang,et al.  Non-fragile robust finite-time H∞ control for nonlinear stochastic itô systems using neural network , 2012 .

[26]  Corentin Briat,et al.  Robust stability and stabilization of uncertain linear positive systems via integral linear constraints: L1‐gain and L∞‐gain characterization , 2012, ArXiv.

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

[28]  Zhengzhi Han,et al.  Absolute exponential stability and stabilization of switched nonlinear systems , 2014, Syst. Control. Lett..

[29]  Y. Chen,et al.  Stability analysis for a class of switched nonlinear systems , 2011, Autom..

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

[31]  Zhong-Ping Jiang,et al.  Uniform Asymptotic Stability of Nonlinear Switched Systems With an Application to Mobile Robots , 2008, IEEE Transactions on Automatic Control.

[32]  Hamid Reza Feyzmahdavian,et al.  Asymptotic Stability and Decay Rates of Homogeneous Positive Systems With Bounded and Unbounded Delays , 2014, SIAM J. Control. Optim..

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

[34]  Peng Shi,et al.  A common linear copositive Lyapunov function for switched positive linear systems with commutable subsystems , 2013, Int. J. Syst. Sci..

[35]  Oliver Mason,et al.  Absolute stability and Lyapunov-Krasovskii functionals for switched nonlinear systems with time-delay , 2014, J. Frankl. Inst..

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

[37]  James Lam,et al.  H ∞  model reduction for discrete‐time positive systems with inhomogeneous initial conditions , 2015 .

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

[39]  Liguo Zhang,et al.  Stability analysis and uniform ultimate boundedness control synthesis for a class of nonlinear switched difference systems , 2012 .