Output tracking control with L1-gain performance for positive switched systems

This paper concentrates on the output tracking control problem with L1-gain performance of positive switched systems. We adopt the multiple co-positive Lyapunov functions technique and conduct the dual design of the controller and the switching signal. Through introducing a new state variable, which is not the output error, the output tracking control problem of the original system is transformed into the stabilization problem of the dynamics system of this new state. The proposed approach is still effective even the output tracking control problem of any subsystem is unsolvable. According to the state being available or not, we establish the solvability conditions of the output tracking control problem for positive switched systems, respectively. In the end, a number example demonstrates the validity of the presented results.

[1]  Lan Shu,et al.  On linear copositive Lyapunov functions for switched positive systems , 2011, J. Frankl. Inst..

[2]  Jun Zhao,et al.  H ∞  output tracking control for discrete‐time switched systems via output feedback , 2015 .

[3]  Xiaojie Su,et al.  Dissipativity-Based Filtering for Fuzzy Switched Systems With Stochastic Perturbation , 2016, IEEE Transactions on Automatic Control.

[4]  Robert Shorten,et al.  On the Stability of Switched Positive Linear Systems , 2007, IEEE Transactions on Automatic Control.

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

[6]  Jun Zhao,et al.  Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings , 2010, Autom..

[7]  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.

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

[9]  Jie Lian,et al.  New results on stability of switched positive systems: an average dwell-time approach , 2013 .

[10]  Juan Wang,et al.  On improving transient performance in tracking control for switched systems with input saturation via composite nonlinear feedback , 2016 .

[11]  Zhengzhi Han,et al.  Robust finite-time stability and stabilisation of switched positive systems , 2014 .

[12]  Mustapha Ait Rami,et al.  Solvability of static output-feedback stabilization for LTI positive systems , 2011, Syst. Control. Lett..

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

[14]  Guo-Ping Liu,et al.  Stability of Systems With Controller Failure and Time-Varying Delay , 2008, IEEE Transactions on Automatic Control.

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

[16]  Zhengrong Xiang,et al.  Exponential L1 output tracking control for positive switched linear systems with time-varying delays , 2014 .

[17]  Huaguang Zhang,et al.  Stabilization of Switched Nonlinear Systems With All Unstable Modes: Application to Multi-Agent Systems , 2011, IEEE Transactions on Automatic Control.

[18]  Jun Fu,et al.  Global finite-time stabilization of a class of switched nonlinear systems with the powers of positive odd rational numbers , 2015, Autom..

[19]  Jian Liang Wang,et al.  Delay-dependent exponential H-infinity filtering for discrete-time switched delay systems , 2012 .

[20]  Peng Shi,et al.  Delay-dependent exponential H ∞ filtering for discrete-time switched delay systems: H ∞ FILTERING FOR DISCRETE-TIME SWITCHED DELAY SYSTEMS , 2012 .

[21]  Huijun Gao,et al.  Approach to stabilisation of continuous-time switched positive systems , 2014 .

[22]  Ligang Wu,et al.  State estimation and sliding mode control for semi-Markovian jump systems with mismatched uncertainties , 2015, Autom..

[23]  Yongduan Song,et al.  Fault Detection Filtering for Nonlinear Switched Stochastic Systems , 2016, IEEE Transactions on Automatic Control.

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

[25]  R. Havira,et al.  Computation of quantized controls using separable programming , 1974 .

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

[27]  Jun Wang,et al.  Passivity of Switched Recurrent Neural Networks With Time-Varying Delays , 2015, IEEE Transactions on Neural Networks and Learning Systems.

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

[29]  Xudong Zhao,et al.  Estimator design of discrete-time switched positive linear systems with average dwell time , 2014, J. Frankl. Inst..

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

[31]  Hamid Reza Karimi,et al.  Asynchronous L1 control of delayed switched positive systems with mode-dependent average dwell time , 2014, Inf. Sci..

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

[33]  Wei Wang,et al.  Integral input-to-state stability for hybrid delayed systems with unstable continuous dynamics , 2012, Autom..

[34]  Xi-Ming Sun,et al.  Asynchronous H∞ control of switched delay systems with average dwell time , 2012, J. Frankl. Inst..

[35]  Ben Niu,et al.  p‐Times differentiable unbounded functions for robust control of uncertain switched nonlinear systems with tracking constraints , 2015 .