Finite-time sampled-data control for switching T-S fuzzy systems

This paper is concerned with the problem of finite-time sampled-data control for switching T-S fuzzy systems. By using the input delay approach, the switching T-S fuzzy systems with variable sampling is transformed into a continuous-time switching T-S fuzzy systems with state-delay. A novel Lyapunov functional is proposed to deal with the problems of finite-time stability (FTS) and finite-time stabilization. Based on the constructed Lyapunov functions and minimum dwell time (MDT) method, new FTS conditions are derived for switching T-S fuzzy systems. Then, according to the FTS conditions, a detailed procedure for designing local sampled-data controllers is given. Finally, an example is provided to illustrate the effectiveness of the proposed design method.

[1]  Francesco Amato,et al.  Finite-time control of discrete-time linear systems , 2005, IEEE Transactions on Automatic Control.

[2]  Guang-Hong Yang,et al.  Dynamic Output Feedback Control Synthesis for Continuous-Time T–S Fuzzy Systems via a Switched Fuzzy Control Scheme , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[3]  Kai-Yuan Cai,et al.  Finite-time quantized guaranteed cost fuzzy control for continuous-time nonlinear systems , 2010, Expert Syst. Appl..

[4]  Euntai Kim,et al.  New approaches to relaxed quadratic stability condition of fuzzy control systems , 2000, IEEE Trans. Fuzzy Syst..

[5]  Hao Liu,et al.  Finite-time stabilization and boundedness of switched linear system under state-dependent switching , 2013, J. Frankl. Inst..

[6]  Young Hoon Joo,et al.  Guaranteed cost sampled‐data fuzzy control for non‐linear systems: a continuous‐time Lyapunov approach , 2013 .

[7]  Francesco Amato,et al.  Finite-Time Stability of Linear Time-Varying Systems: Analysis and Controller Design , 2010, IEEE Transactions on Automatic Control.

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

[9]  Wen-an Zhang,et al.  Stabilization of Sampled-Data Control Systems With Control Inputs Missing , 2010, IEEE Transactions on Automatic Control.

[10]  Jian Xiao,et al.  H∞ finite-time control for switched nonlinear discrete-time systems with norm-bounded disturbance , 2011, J. Frankl. Inst..

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

[12]  GaoHuijun,et al.  Stabilization of Nonlinear Systems Under Variable Sampling , 2007 .

[13]  Alexandre Seuret,et al.  Stability Analysis of Sampled-Data Systems Using Sum of Squares , 2013, IEEE Transactions on Automatic Control.

[14]  Emilia Fridman,et al.  A refined input delay approach to sampled-data control , 2010, Autom..

[15]  Jun Yoneyama,et al.  Robust H∞ control of uncertain fuzzy systems under time-varying sampling , 2010, Fuzzy Sets Syst..

[16]  TanakaK.,et al.  Fuzzy regulators and fuzzy observers , 1998 .

[17]  Hamid Reza Karimi,et al.  Novel Stability Criteria for T--S Fuzzy Systems , 2014, IEEE Transactions on Fuzzy Systems.

[18]  Hak-Keung Lam,et al.  Sampled-Data Fuzzy Controller for Time-Delay Nonlinear Systems: Fuzzy-Model-Based LMI Approach , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[19]  Kazuo Tanaka,et al.  Stability and smoothness conditions for switching fuzzy systems , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[20]  Francesco Amato,et al.  Finite-time control of linear systems subject to parametric uncertainties and disturbances , 2001, Autom..

[21]  Ying-Xu Yang,et al.  Finite-time stability and stabilization of nonlinear stochastic hybrid systems☆ , 2009 .

[22]  Huijun Gao,et al.  Stabilization of Nonlinear Systems Under Variable Sampling: A Fuzzy Control Approach , 2007, IEEE Transactions on Fuzzy Systems.

[23]  Kun Liu,et al.  Wirtinger's inequality and Lyapunov-based sampled-data stabilization , 2012, Autom..

[24]  Mohammad N. ElBsat,et al.  Robust and resilient finite-time bounded control of discrete-time uncertain nonlinear systems , 2013, Autom..

[25]  Francesco Amato,et al.  Finite-time control of discrete-time linear systems: Analysis and design conditions , 2010, Autom..

[26]  Kazuo Tanaka,et al.  Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs , 1998, IEEE Trans. Fuzzy Syst..

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

[28]  Graham C. Goodwin,et al.  On sampled-data models for nonlinear systems , 2005, IEEE Transactions on Automatic Control.

[29]  Shen Yin,et al.  Switching Stabilization for a Class of Slowly Switched Systems , 2015, IEEE Transactions on Automatic Control.

[30]  H. K. Lam,et al.  Stability analysis of sampled-data fuzzy controller for nonlinear systems based on switching T–S fuzzy model , 2009 .

[31]  Zhengrong Xiang,et al.  Robust reliable stabilization of stochastic switched nonlinear systems under asynchronous switching , 2011, Appl. Math. Comput..

[32]  Shihua Li,et al.  Finite-time boundedness and stabilization of switched linear systems , 2010, Kybernetika.

[33]  Hak-Keung Lam,et al.  Stabilization of Nonlinear Systems Using Sampled-Data Output-Feedback Fuzzy Controller Based on Polynomial-Fuzzy-Model-Based Control Approach , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[34]  El Houssaine Tissir,et al.  Exponential Stability of Uncertain T-S Fuzzy Switched Systems with Time Delay , 2013, Int. J. Autom. Comput..

[35]  Ming Cao,et al.  Dwell-time switching , 2010, Syst. Control. Lett..

[36]  Chieh-Li Chen,et al.  Analysis and design of fuzzy control system , 1993 .

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

[38]  Emilia Fridman,et al.  Robust sampled-data stabilization of linear systems: an input delay approach , 2004, Autom..

[39]  Shengyuan Xu,et al.  The Exponential Stability and Asynchronous Stabilization of a Class of Switched Nonlinear System Via the T–S Fuzzy Model , 2014, IEEE Transactions on Fuzzy Systems.

[40]  Wei Xing Zheng,et al.  Delay-Independent Minimum Dwell Time for Exponential Stability of Uncertain Switched Delay Systems , 2010, IEEE Transactions on Automatic Control.