Stochastic sampled data robust stabilisation of T-S fuzzy neutral systems with randomly occurring uncertainties and time-varying delays

This paper is concerned with the stochastic sampled data robust stabilisation of T-S fuzzy neutral systems with randomly occurring uncertainties and time-varying delays. The sampling period is assumed to be m in number, whose occurrence probabilities are given constants and satisfy Bernoulli distribution. By introducing an improved Lyapunov–Krasovskii functional with new triple integral terms and by combining both the convex combination technique and reciprocal convex technique, delay-dependent robust stability criteria are obtained in terms of linear matrix inequalities. These linear matrix inequalities can be easily solved by using standard convex optimisation algorithms. The designed stochastic sampled data fuzzy controller gain can be obtained. Finally, three numerical examples are given to illustrate the effectiveness of the proposed methods.

[1]  Huaguang Zhang,et al.  An enhanced input-delay approach to sampled-data stabilization of T–S fuzzy systems via mixed convex combination , 2014 .

[2]  Masayoshi Tomizuka,et al.  Fuzzy Stabilization of Nonlinear Systems under Sampled-Data Feedback: An Exact Discrete-Time Model Approach , 2010, IEEE Transactions on Fuzzy Systems.

[3]  Jianbin Qiu,et al.  Fuzzy-Model-Based Piecewise ${\mathscr H}_{\infty }$ Static-Output-Feedback Controller Design for Networked Nonlinear Systems , 2010, IEEE Transactions on Fuzzy Systems.

[4]  Shaocheng Tong,et al.  Adaptive fuzzy backstepping output feedback control of nonlinear uncertain time-delay systems based on high-gain filters , 2012 .

[5]  Huijun Gao,et al.  Stabilization of Networked Control Systems With a New Delay Characterization , 2008, IEEE Transactions on Automatic Control.

[6]  P. Balasubramaniam,et al.  Delay-range-dependent robust stabilisation and H ∞ control for nonlinear uncertain stochastic fuzzy systems with mode-dependent time delays and Markovian jump parameters , 2013, Int. J. Syst. Sci..

[7]  Tae H. Lee,et al.  Stochastic sampled-data control for state estimation of time-varying delayed neural networks , 2013, Neural Networks.

[8]  B. Pasik-Duncan,et al.  Adaptive Control , 1996, IEEE Control Systems.

[9]  Yong-Yan Cao,et al.  Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach , 2000, IEEE Trans. Fuzzy Syst..

[10]  Zidong Wang,et al.  Sampled-Data Synchronization Control of Dynamical Networks With Stochastic Sampling , 2012, IEEE Transactions on Automatic Control.

[11]  Jun Yoneyama,et al.  Robust stability and stabilizing controller design of fuzzy systems with discrete and distributed delays , 2008, Inf. Sci..

[12]  Ju H. Park,et al.  Synchronization of a complex dynamical network with coupling time-varying delays via sampled-data control , 2012, Appl. Math. Comput..

[13]  PooGyeon Park,et al.  Reciprocally convex approach to stability of systems with time-varying delays , 2011, Autom..

[14]  Jun Hu,et al.  Robust Sliding Mode Control for Discrete Stochastic Systems With Mixed Time Delays, Randomly Occurring Uncertainties, and Randomly Occurring Nonlinearities , 2012, IEEE Transactions on Industrial Electronics.

[15]  Huijun Gao,et al.  Robust Sampled-Data $H_{\infty}$ Control for Vehicle Active Suspension Systems , 2010, IEEE Transactions on Control Systems Technology.

[16]  Z. Zeng,et al.  Robust H∞ output tracking control for fuzzy networked systems with stochastic sampling and multiplicative noise , 2012 .

[17]  Jianbin Qiu,et al.  Observer-Based Piecewise Affine Output Feedback Controller Synthesis of Continuous-Time T–S Fuzzy Affine Dynamic Systems Using Quantized Measurements , 2012, IEEE Transactions on Fuzzy Systems.

[18]  A. N. Michel,et al.  Stability analysis of digital feedback control systems with time-varying sampling periods , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[19]  Shouming Zhong,et al.  Improved delay-dependent stability criterion for neural networks with time-varying delay , 2011, Appl. Math. Comput..

[20]  Zhang Qing-ling,et al.  Stochastic stability of networked control systems with time-varying sampling periods , 2009 .

[21]  R. Rakkiyappan,et al.  Delay-dependent robust exponential state estimation of Markovian jumping fuzzy Hopfield neural networks with mixed random time-varying delays , 2011 .

[22]  Ju H. Park,et al.  Robust sampled-data control with random missing data scenario , 2014, Int. J. Control.

[23]  PooGyeon Park,et al.  Robust Η/ spl alpha/ stabilisation of networked control systems with packet analyser [Brief Paper] , 2010 .

[24]  Jianbin Qiu,et al.  A New Design of Delay-Dependent Robust ${\cal H}_{\bm \infty}$ Filtering for Discrete-Time T--S Fuzzy Systems With Time-Varying Delay , 2009, IEEE Transactions on Fuzzy Systems.

[25]  Changyin Sun,et al.  Improved delay-dependent stability criteria for neural networks with time-varying delay , 2008, WCICA 2008.

[26]  Hak-Keung Lam,et al.  Stabilization of Chaotic Systems Using Linear sampled-Data Controller , 2007, Int. J. Bifurc. Chaos.

[27]  Huijun Gao,et al.  Robust sampled-data H∞ control with stochastic sampling , 2009, Autom..

[28]  Dianhui Wang,et al.  Quadratically convex combination approach to stability of T-S fuzzy systems with time-varying delay , 2014, J. Frankl. Inst..

[29]  Haibo Wang,et al.  Observer-based H∞ control for discrete-time T-S fuzzy systems , 2009, 2009 Chinese Control and Decision Conference.

[30]  P. Balasubramaniam,et al.  Delay-dependent robust H ∞ control for uncertain stochastic T–S fuzzy systems with time-varying state and input delays , 2011, Int. J. Syst. Sci..

[31]  Jun Hu,et al.  Robust Sliding Mode Control for Discrete Stochastic Systems with Mixed Time-delays , Randomly Occurring Uncertainties and Nonlinearities , 2011 .

[32]  Engang Tian,et al.  Sampled-data robust H∞ control for T-S fuzzy systems with time delay and uncertainties , 2011, Fuzzy Sets Syst..

[33]  Shun-Hung Tsai,et al.  Delay-dependent robust stabilisation for a class of fuzzy bilinear systems with time-varying delays in state and control input , 2014, Int. J. Syst. Sci..

[34]  Bo Song,et al.  Exponential synchronization for complex dynamical networks with sampled-data , 2012, J. Frankl. Inst..

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

[36]  Ju H. Park,et al.  New approaches on stability criteria for neural networks with interval time-varying delays , 2012, Appl. Math. Comput..

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

[38]  Stuart Townley,et al.  Integral control by variable sampling based on steady-state data , 2003, Autom..

[39]  Jianbin Qiu,et al.  Asynchronous Output-Feedback Control of Networked Nonlinear Systems With Multiple Packet Dropouts: T–S Fuzzy Affine Model-Based Approach , 2011, IEEE Transactions on Fuzzy Systems.

[40]  E. Fridman,et al.  Input / output delay approach to robust sampled-data H ∞ control , 2005 .

[41]  Andreas Mueller.  Recent Advances in Robust Control - Novel Approaches and Design Methods , 2011 .

[42]  Ligang Wu,et al.  A New Approach to Stability Analysis and Stabilization of Discrete-Time T-S Fuzzy Time-Varying Delay Systems , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[43]  Shaocheng Tong,et al.  New delay-dependent stabilization conditions of T-S fuzzy systems with constant delay , 2007, Fuzzy Sets Syst..

[44]  Tao Zhang,et al.  Robust stabilisation of uncertain systems with interval time-varying state and input delays , 2009, Int. J. Syst. Sci..

[45]  Ju H. Park,et al.  Robust synchronisation of chaotic systems with randomly occurring uncertainties via stochastic sampled-data control , 2013, Int. J. Control.

[46]  Shengyuan Xu,et al.  Robust stabilization and H∞ control for uncertain fuzzy neutral systems with mixed time delays , 2008, Fuzzy Sets Syst..

[47]  Huaguang Zhang,et al.  T-S Model-based Relaxed Reliable Stabilization of Networked Control Systems with Time-varying Delays under Variable Sampling , 2011 .

[48]  Tong Heng Lee,et al.  Delay-dependent LMI conditions for stability and stabilization of T-S fuzzy systems with bounded time-delay , 2006, Fuzzy Sets Syst..

[49]  Huaguang Zhang,et al.  Mode-independent fuzzy fault-tolerant variable sampling stabilization of nonlinear networked systems with both time-varying and random delays , 2012, Fuzzy Sets Syst..

[50]  Jun Yoneyama,et al.  Robust stability and stabilization for uncertain Takagi-Sugeno fuzzy time-delay systems , 2007, Fuzzy Sets Syst..