Asynchronous L1 control of delayed switched positive systems with mode-dependent average dwell time

Abstract This paper investigates the stability and asynchronous L 1 control problems for a class of switched positive linear systems (SPLSs) with time-varying delays by using the mode-dependent average dwell time (MDADT) approach. By allowing the co-positive type Lyapunov–Krasovskii functional to increase during the running time of active subsystems, a new stability criterion for the underlying system with MDADT is first derived. Then, the obtained results are extended to study the issue of asynchronous L 1 control, where “asynchronous” means that the switching of the controllers has a lag with respect to that of system modes. Sufficient conditions are provided to guarantee that the resulting closed-loop system is exponentially stable and has an L 1 -gain performance. Finally, two numerical examples are given to show the effectiveness of the developed results.

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

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

[3]  Huijun Gao,et al.  Network-based feedback control for systems with mixed delays based on quantization and dropout compensation , 2011, Autom..

[4]  Ligang Wu,et al.  Sensor Networks With Random Link Failures: Distributed Filtering for T–S Fuzzy Systems , 2013, IEEE Transactions on Industrial Informatics.

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

[6]  Ye Zhao,et al.  Asynchronous Filtering of Discrete-Time Switched Linear Systems With Average Dwell Time , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

[8]  Ettore Fornasini,et al.  Linear Copositive Lyapunov Functions for Continuous-Time Positive Switched Systems , 2010, IEEE Transactions on Automatic Control.

[9]  Wei Xing Zheng,et al.  Weighted H∞ model reduction for linear switched systems with time-varying delay , 2009, Autom..

[10]  Yongduan Song,et al.  A Novel Control Design on Discrete-Time Takagi–Sugeno Fuzzy Systems With Time-Varying Delays , 2013, IEEE Transactions on Fuzzy Systems.

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

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

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

[14]  Patrizio Colaneri,et al.  Stabilization of continuous-time switched linear positive systems , 2010, Proceedings of the 2010 American Control Conference.

[15]  Guo-Ping Liu,et al.  Filtering for Discrete-Time Networked Nonlinear Systems With Mixed Random Delays and Packet Dropouts , 2011, IEEE Transactions on Automatic Control.

[16]  Peng Shi,et al.  Delay‐dependent robust H∞ control for uncertain stochastic time‐delay systems , 2010 .

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

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

[19]  Ettore Fornasini,et al.  Stability and Stabilizability Criteria for Discrete-Time Positive Switched Systems , 2012, IEEE Transactions on Automatic Control.

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

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

[22]  Stability , 1973 .

[23]  Kou Yamada,et al.  LINEAR MATRIX INEQUALITY-BASED REPETITIVE CONTROLLER DESIGN FOR LINEAR SYSTEMS WITH TIME-VARYING UNCERTAINTIES TO REJECT POSITION-DEPENDENT DISTURBANCES , 2013 .

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

[25]  Yongduan Song,et al.  A Novel Approach to Filter Design for T–S Fuzzy Discrete-Time Systems With Time-Varying Delay , 2012, IEEE Transactions on Fuzzy Systems.

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

[27]  Ligang Wu,et al.  Output Feedback Control of Markovian Jump Repeated Scalar Nonlinear Systems , 2014, IEEE Transactions on Automatic Control.

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

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

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

[31]  Wei Wang,et al.  NEW RESULTS ON MODEL REDUCTION FOR DISCRETE-TIME SWITCHED SYSTEMS WITH TIME DELAY , 2012 .

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

[33]  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.

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

[35]  Yun Chen,et al.  Delay-Dependent Robust Control for Uncertain Stochastic Time-Delay Systems , 2008 .

[36]  M. Suárez-Castañón,et al.  A SWITCHING CONTROLLER FOR THE STABILIZATION OF THE DAMPING INVERTED PENDULUM CART SYSTEM , 2013 .

[37]  B. C. Brookes,et al.  Information Sciences , 2020, Cognitive Skills You Need for the 21st Century.

[38]  S. B. Attia,et al.  STATIC SWITCHED OUTPUT FEEDBACK STABILIZATION FOR LINEAR DISCRETE-TIME SWITCHED SYSTEMS , 2012 .

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

[40]  Wei Xing Zheng,et al.  Dissipativity-Based Sliding Mode Control of Switched Stochastic Systems , 2013, IEEE Transactions on Automatic Control.

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