Exponential stabilization of nonlinear switched systems with distributed time-delay: An average dwell time approach

Abstract In this paper, the exponential stabilization problem is discussed for nonlinear switched systems subject to the distributed time-delay. Attention is focused on the design of a state feedback controller such that, the closed-loop system is exponentially stable with a guaranteed weighted L 2 gain. By resorting to the average dwell time method and the piecewise Lyapunov functional approach, sufficient conditions are derived for the solvability of the addressed problem in terms of the feasibility of certain Hamilton–Jacobi inequalities (HJIs). The explicit expression of the desired controller is formulated via solving the presented set of HJIs. Furthermore, within the proposed framework, the exponential stabilization problems are investigated, respectively, for nonlinear switched systems with mixed time-delays and linear switched systems with the distributed time-delay. Finally, a simulation example is given to illustrate the effectiveness and applicability of the proposed algorithm.

[1]  Fuad E. Alsaadi,et al.  Robust filtering for a class of nonlinear stochastic systems with probability constraints , 2016, Autom. Remote. Control..

[2]  Hamid Reza Karimi.  A computational method for optimal control problem of time-varying state-delayed systems by Haar wavelets , 2006, Int. J. Comput. Math..

[3]  M.D.S. Aliyu,et al.  Dissipativity and stability of nonlinear jump systems , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[4]  Hamid Reza Karimi,et al.  New Delay-Dependent Exponential $H_{\infty}$ Synchronization for Uncertain Neural Networks With Mixed Time Delays , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[5]  Jamal Daafouz,et al.  Switched state-feedback control for continuous time-varying polytopic systems , 2011, Int. J. Control.

[6]  Mohamed Darouach,et al.  Robust admissibility of uncertain switched singular systems , 2011, Int. J. Control.

[7]  Damien Koenig,et al.  Unknown Input Observers for Switched Nonlinear Discrete Time Descriptor Systems , 2008, IEEE Transactions on Automatic Control.

[8]  Yonggang Chen,et al.  Stabilization of neutral time-delay systems with actuator saturation via auxiliary time-delay feedback , 2015, Autom..

[9]  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.

[10]  Christopher Edwards,et al.  Adaptive continuous higher order sliding mode control , 2016, Autom..

[11]  Weihai Zhang,et al.  State Feedback HINFINITY Control for a Class of Nonlinear Stochastic Systems , 2006, SIAM J. Control. Optim..

[12]  João Pedro Hespanha,et al.  Switching between stabilizing controllers , 2002, Autom..

[13]  Fuad E. Alsaadi,et al.  H∞ and I2-I∞ finite-horizon filtering with randomly occurring gain variations and quantization effects , 2017, Appl. Math. Comput..

[14]  Zidong Wang,et al.  Event-based state estimation for a class of complex networks with time-varying delays: A comparison principle approach , 2017 .

[15]  Piyapong Niamsup,et al.  Novel criteria for finite-time stabilization and guaranteed cost control of delayed neural networks , 2015, Neurocomputing.

[16]  Murad Abu-Khalaf,et al.  Nonlinear H2/H∞ Constrained Feedback Control: A Practical Design Approach Using Neural Networks , 2007 .

[17]  Shuxiang Guo,et al.  Robust reliability method for non-fragile guaranteed cost control of parametric uncertain systems , 2014, Syst. Control. Lett..

[18]  K. Gu.  An integral inequality in the stability problem of time-delay systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[19]  Hamid Reza Karimi,et al.  Robust Delay-Dependent $H_{\infty}$ Control of Uncertain Time-Delay Systems With Mixed Neutral, Discrete, and Distributed Time-Delays and Markovian Switching Parameters , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[20]  Lei Guo,et al.  Resilient Control of Networked Control System Under DoS Attacks: A Unified Game Approach , 2016, IEEE Transactions on Industrial Informatics.

[21]  Kazuo Tanaka,et al.  A Sum-of-Squares Approach to Modeling and Control of Nonlinear Dynamical Systems With Polynomial Fuzzy Systems , 2009, IEEE Transactions on Fuzzy Systems.

[22]  Yurong Liu,et al.  Exponential stability of Markovian jumping Cohen-Grossberg neural networks with mixed mode-dependent time-delays , 2016, Neurocomputing.

[23]  Fuad E. Alsaadi,et al.  A Resilient Approach to Distributed Filter Design for Time-Varying Systems Under Stochastic Nonlinearities and Sensor Degradation , 2017, IEEE Transactions on Signal Processing.

[24]  Shuai Liu,et al.  Extended Kalman filtering for stochastic nonlinear systems with randomly occurring cyber attacks , 2016, Neurocomputing.

[25]  Yonggang Chen,et al.  Improved robust stability conditions for uncertain neutral systems with discrete and distributed delays , 2015, J. Frankl. Inst..

[26]  Shuai Liu,et al.  Error-constrained reliable tracking control for discrete time-varying systems subject to quantization effects , 2016, Neurocomputing.

[27]  Chenglin Wen,et al.  A reduced-order approach to filtering for systems with linear equality constraints , 2016, Neurocomputing.

[28]  Hamid Reza Karimi,et al.  Numerically efficient approximations to the optimal control of linear singularly perturbed systems based on Haar wavelets , 2005, Int. J. Comput. Math..

[29]  Yunlong Liu,et al.  Input-to-state stability for discrete-time nonlinear switched singular systems , 2016, Inf. Sci..

[30]  Jianbin Qiu,et al.  A Switched System Approach to Exponential Stabilization of Sampled-Data T–S Fuzzy Systems With Packet Dropouts , 2016, IEEE Transactions on Cybernetics.

[31]  Gregory Hagen,et al.  Spillover Stabilization in Finite-Dimensional Control and Observer Design for Dissipative Evolution Equations , 2003, SIAM J. Control. Optim..

[32]  Fuad E. Alsaadi,et al.  A new framework for output feedback controller design for a class of discrete-time stochastic nonlinear system with quantization and missing measurement , 2016, Int. J. Gen. Syst..

[33]  Mohammed Chadli,et al.  A sum of squares approach for polynomial fuzzy observer design for polynomial fuzzy systems with unknown inputs , 2016 .

[34]  Fuad E. Alsaadi,et al.  Event-triggered H ∞ state estimation for discrete-time stochastic genetic regulatory networks with Markovian jumping parameters and time-varying delays , 2016, Neurocomputing.

[35]  Yurong Liu,et al.  Passivity analysis for discrete-time neural networks with mixed time-delays and randomly occurring quantization effects , 2016, Neurocomputing.

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

[37]  Paul M. Frank,et al.  Robust control of uncertain distributed delay systems with application to the stabilization of combustion in rocket motor chambers , 2002, Autom..

[38]  Hamid Reza Karimi,et al.  A structured filter for Markovian switching systems , 2014, Int. J. Syst. Sci..

[39]  T. Senthilkumar.  Robust stabilization and H ∞ control for nonlinear stochastic T-S fuzzy Markovian jump systems with mixed time-varying delays and linear fractional uncertainties , 2016, Neurocomputing.

[40]  M. Branicky.  Multiple Lyapunov functions and other analysis tools for switched and hybrid systems , 1998, IEEE Trans. Autom. Control..

[41]  M. Darouach,et al.  Admissibility and control of switched discrete-time singular systems , 2013 .

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

[43]  Zidong Wang,et al.  A game theory approach to mixed H2/H∞ control for a class of stochastic time-varying systems with randomly occurring nonlinearities , 2011, Syst. Control. Lett..

[44]  Yuangong Sun,et al.  Stabilization of Switched Systems With Nonlinear Impulse Effects and Disturbances , 2011, IEEE Transactions on Automatic Control.