Reliable $H_{\infty}$ Nonuniform Sampling Fuzzy Control for Nonlinear Systems With Time Delay

The problem of reliable H infin nonuniform sampling fuzzy control for nonlinear systems with time delay is investigated in this paper. Utilizing the input delay approach and the descriptor model transformation, an equivalent continuous-time generalized Takagi-Sugeno fuzzy system is obtained. Sufficient conditions for the existence of state feedback controller are derived in terms of linear matrix inequities (LMIs), which guarantee the requirements of H infin performance criterion for the normal and possible actuator fault cases. In order to relax the conservatism of these obtained conditions, a feasible algorithm is provided to remove some slightly restricted conditions in LMIs. Finally, an illustrative example is given to show the validity of the proposed scheme.

[1]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[2]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[3]  L. Ghaoui,et al.  A cone complementarity linearization algorithm for static output-feedback and related problems , 1996, Proceedings of Joint Conference on Control Applications Intelligent Control and Computer Aided Control System Design.

[4]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[5]  Bor-Sen Chen,et al.  Mixed H2/H∞ fuzzy output feedback control design for nonlinear dynamic systems: an LMI approach , 2000, IEEE Trans. Fuzzy Syst..

[6]  Geir E. Dullerud,et al.  An LMI solution to the robust synthesis problem for multi-rate sampled-data systems , 2001, Autom..

[7]  Kazuo Tanaka,et al.  Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach , 2008 .

[8]  Emilia Fridman,et al.  An improved stabilization method for linear time-delay systems , 2002, IEEE Trans. Autom. Control..

[9]  J. Lam,et al.  Reliable H control of uncertain descriptor systems with multiple time delays , 2003 .

[10]  James Lam,et al.  A linear matrix inequality (LMI) approach to robust H/sub 2/ sampled-data control for linear uncertain systems. , 2003, IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society.

[11]  Huijun Gao,et al.  Comments and further results on "A descriptor system approach to H∞ control of linear time-delay systems" , 2003, IEEE Trans. Autom. Control..

[12]  Huai-Ning Wu,et al.  Reliable LQ fuzzy control for nonlinear discrete-time systems via LMIs , 2004, IEEE Trans. Syst. Man Cybern. Part B.

[13]  Guo-Ping Liu,et al.  Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties , 2004, IEEE Transactions on Automatic Control.

[14]  Bing Chen,et al.  Reliable control design of fuzzy dynamic systems with time-varying delay , 2004, Fuzzy Sets Syst..

[15]  Akira Ichikawa,et al.  Hinfinity control for sampled-data nonlinear systems described by Takagi-Sugeno fuzzy systems , 2004, Fuzzy Sets Syst..

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

[17]  Q. Han,et al.  State feedback controller design of networked control systems , 2004 .

[18]  B. Chen,et al.  Delay-Dependent Robust H∞ Control for T-S Fuzzy Systems With Time Delay , 2005, IEEE Trans. Fuzzy Syst..

[19]  Biao Huang,et al.  Multirate Robust Digital Control for Fuzzy Systems With Periodic Lyapunov Function , 2005, IEEE Trans. Fuzzy Syst..

[20]  Hak-Keung Lam,et al.  Design and stabilization of sampled-data neural-network-based control systems , 2005 .

[21]  Dong Yue,et al.  Delayed feedback control of uncertain systems with time-varying input delay , 2005, Autom..

[22]  Engang Tian,et al.  Delay-dependent stability analysis and synthesis of uncertain T-S fuzzy systems with time-varying delay , 2006, Fuzzy Sets Syst..

[23]  Guang-Hong Yang,et al.  Adaptive Fault-Tolerant Tracking Control Against Actuator Faults With Application to Flight Control , 2006, IEEE Transactions on Control Systems Technology.

[24]  Huai-Ning Wu,et al.  Reliable$rm H_infty $Fuzzy Control for Continuous-Time Nonlinear Systems With Actuator Failures , 2006, IEEE Transactions on Fuzzy Systems.

[25]  Huaguang Zhang,et al.  Fuzzy $H_\infty$ Filter Design for a Class of Nonlinear Discrete-Time Systems With Multiple Time Delays , 2007, IEEE Transactions on Fuzzy Systems.

[26]  Jin Bae Park,et al.  Effective digital implementation of fuzzy control systems based on approximate discrete-time models , 2007, Autom..

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

[28]  Huai-Ning Wu,et al.  Reliable ${H}_{\infty}$ Fuzzy Control for a Class of Discrete-Time Nonlinear Systems Using Multiple Fuzzy Lyapunov Functions , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[29]  Jun Yang,et al.  T-S Fuzzy-Model-Based Robust $H_{\infty}$ Design for Networked Control Systems With Uncertainties , 2007, IEEE Transactions on Industrial Informatics.

[30]  Qing-Long Han,et al.  Robust $H_{\infty}$ Control for Uncertain Takagi–Sugeno Fuzzy Systems With Interval Time-Varying Delay , 2007, IEEE Transactions on Fuzzy Systems.

[31]  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).

[32]  Huaguang Zhang,et al.  Guaranteed Cost Networked Control for T–S Fuzzy Systems With Time Delays , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).