Control Design for Discrete-Time Fuzzy Systems with Disturbance Inputs via Delta Operator Approach

This paper is concerned with the problem of passive control design for discrete-time Takagi-Sugeno (T-S) fuzzy systems with time delay and disturbance input via delta operator approach. The discrete-time passive performance index is established in this paper for the control design problem. By constructing a new type ofLyapunov-Krasovskii function (LKF) in delta domain, and utilizing some fuzzy weighing matrices, a new passive performance condition is proposed for the system under consideration. Based on the condition, a state-feedback passive controller is designed to guarantee that the resulting closed-loop system is very-strictly passive. The existence conditions of the controller can be expressed by linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate the feasibility and effectiveness of the proposed method.

[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]  Graham C. Goodwin,et al.  Rapprochement between continuous and discrete model reference adaptive control , 1986, Autom..

[3]  G. Goodwin,et al.  Improved finite word length characteristics in digital control using delta operators , 1986 .

[4]  Charles P. Neuman,et al.  Transformations between delta and forward shift operator transfer function models , 1993, IEEE Trans. Syst. Man Cybern..

[5]  Kamal Premaratne,et al.  Delta-operator formulated discrete-time approximations of continuous-time systems , 1994, IEEE Trans. Autom. Control..

[6]  Kamal Premaratne,et al.  Tabular method for determining root distribution of delta-operator formulated real polynomials , 1994, IEEE Trans. Autom. Control..

[7]  M. M'Saad,et al.  Discrete-time compensators with loop transfer recovery , 1994 .

[8]  Lihua Xie,et al.  Output feedback H∞ control of systems with parameter uncertainty , 1996 .

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

[10]  Kazuo Tanaka,et al.  Fuzzy control systems design and analysis , 2001 .

[11]  P. Shi,et al.  Fuzzy Output Feedback Control Design for Nonlinear Systems: An LMI Approach , 2003 .

[12]  Kazuo Tanaka,et al.  A multiple Lyapunov function approach to stabilization of fuzzy control systems , 2003, IEEE Trans. Fuzzy Syst..

[13]  Peng Shi,et al.  H∞ fuzzy output feedback control design for nonlinear systems: an LMI approach , 2003, IEEE Trans. Fuzzy Syst..

[14]  Thierry-Marie Guerra,et al.  LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form , 2004, Autom..

[15]  Xiefu Jiang,et al.  Stability criteria for linear discrete-time systems with interval-like time-varying delay , 2005, Proceedings of the 2005, American Control Conference, 2005..

[16]  Tong Heng Lee,et al.  Stabilization of uncertain fuzzy time-delay systems via variable structure control approach , 2005, IEEE Transactions on Fuzzy Systems.

[17]  J. Lam,et al.  Title Robust H ∞ control for uncertain discrete-time-delay fuzzysystems via output feedback controllers , 2005 .

[18]  G. Feng,et al.  A Survey on Analysis and Design of Model-Based Fuzzy Control Systems , 2006, IEEE Transactions on Fuzzy Systems.

[19]  Xiaofeng Liao,et al.  Passivity and Passification of Fuzzy Systems with Time Delays , 2006, Comput. Math. Appl..

[20]  Tong Heng Lee,et al.  LMI Approach to Analysis and Control of Takagi-Sugeno Fuzzy Systems with Time Delay (Lecture Notes in Control and Information Sciences) , 2007 .

[21]  Shaocheng Tong,et al.  Guaranteed cost control of T-S fuzzy systems with state and input delays , 2007, Fuzzy Sets Syst..

[22]  Huijun Gao,et al.  Passivity and Passification for Networked Control Systems , 2007, SIAM J. Control. Optim..

[23]  P. Shi,et al.  Robust H1 control design for fuzzy singularly perturbed systems with Markovian jumps: an LMI approach , 2007 .

[24]  J. Qiu,et al.  Robust stabilisation for a class of discrete-time systems with time-varying delays via delta operators , 2008 .

[25]  Shengyuan Xu,et al.  Delay-Dependent Robust $\hbox{\it H}_\infty$ Control for Uncertain Discrete-Time Fuzzy Systems With Time-Varying Delays , 2009, IEEE Transactions on Fuzzy Systems.

[26]  Shaocheng Tong,et al.  Observer-based fuzzy adaptive control for strict-feedback nonlinear systems , 2009, Fuzzy Sets Syst..

[27]  Shengyuan Xu,et al.  Robust stabilization of uncertain T-S fuzzy time-delay systems with exponential estimates , 2009, Fuzzy Sets Syst..

[28]  Shaocheng Tong,et al.  A Combined Backstepping and Small-Gain Approach to Robust Adaptive Fuzzy Output Feedback Control , 2009, IEEE Transactions on Fuzzy Systems.

[29]  Wei Xing Zheng,et al.  Passivity-based sliding mode control of uncertain singular time-delay systems , 2009, Autom..

[30]  Xiaoping Liu,et al.  Robust Hinfinity control of Takagi-Sugeno fuzzy systems with state and input time delays , 2009, Fuzzy Sets Syst..

[31]  Shengyuan Xu,et al.  Passivity Analysis of Neural Networks With Time-Varying Delays , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[32]  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.

[33]  Zehui Mao,et al.  $H_\infty$-Filter Design for a Class of Networked Control Systems Via T–S Fuzzy-Model Approach , 2010, IEEE Transactions on Fuzzy Systems.

[34]  Zidong Wang,et al.  On Passivity and Passification of Stochastic Fuzzy Systems With Delays: The Discrete-Time Case , 2010, IEEE Trans. Syst. Man Cybern. Part B.

[35]  Daniel W. C. Ho,et al.  Robust $H_{\infty }$ Fuzzy Output-Feedback Control With Multiple Probabilistic Delays and Multiple Missing Measurements , 2010, IEEE Transactions on Fuzzy Systems.

[36]  Huijun Gao,et al.  New Passivity Analysis for Neural Networks With Discrete and Distributed Delays , 2010, IEEE Transactions on Neural Networks.

[37]  Yuanqing Xia,et al.  Observer-based sliding mode control for a class of discrete systems via delta operator approach , 2010, J. Frankl. Inst..

[38]  Hak-Keung Lam,et al.  Polynomial Fuzzy-Model-Based Control Systems: Stability Analysis Via Piecewise-Linear Membership Functions , 2011, IEEE Transactions on Fuzzy Systems.

[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]  Peng Shi,et al.  Passivity Analysis for Discrete-Time Stochastic Markovian Jump Neural Networks With Mixed Time Delays , 2011, IEEE Transactions on Neural Networks.

[41]  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).

[42]  Jianbin Qiu,et al.  Model Approximation for Discrete-Time State-Delay Systems in the T–S Fuzzy Framework , 2011, IEEE Transactions on Fuzzy Systems.

[43]  Shengyuan Xu,et al.  Passivity analysis and passive control of fuzzy systems with time-varying delays , 2011, Fuzzy Sets Syst..

[44]  Peng Shi,et al.  Robust H∞ control for a class of discrete time fuzzy systems via delta operator approach , 2012, Inf. Sci..

[45]  Honghai Liu,et al.  Reliable Fuzzy Control for Active Suspension Systems With Actuator Delay and Fault , 2012, IEEE Transactions on Fuzzy Systems.

[46]  Shaocheng Tong,et al.  Adaptive fuzzy output feedback control of uncertain nonlinear systems with unknown backlash-like hysteresis , 2012, Inf. Sci..

[47]  Peng Shi,et al.  Fuzzy-Model-Based Fault-Tolerant Design for Nonlinear Stochastic Systems Against Simultaneous Sensor and Actuator Faults , 2013, IEEE Transactions on Fuzzy Systems.

[48]  Yi Shen,et al.  Passive Control for Stochastic Interval Systems with Interval Time‐Varying Delay , 2013 .

[49]  Peng Shi,et al.  Fault Estimation and Tolerant Control for Fuzzy Stochastic Systems , 2013, IEEE Transactions on Fuzzy Systems.

[50]  Hak-Keung Lam,et al.  Membership-function-dependent stability analysis of fuzzy-model-based control systems using fuzzy Lyapunov functions , 2013, Inf. Sci..

[51]  Hak-Keung Lam,et al.  Output Regulation of Polynomial-Fuzzy-Model-Based Control Systems , 2013, IEEE Transactions on Fuzzy Systems.

[52]  Honghai Liu,et al.  Adaptive Sliding-Mode Control for Nonlinear Active Suspension Vehicle Systems Using T–S Fuzzy Approach , 2013, IEEE Transactions on Industrial Electronics.

[53]  Steven X. Ding,et al.  Real-Time Implementation of Fault-Tolerant Control Systems With Performance Optimization , 2014, IEEE Transactions on Industrial Electronics.

[54]  李永明,et al.  Adaptive fuzzy robust output feedback control of nonlinear systems with unknown dead zones based on small-gain approach , 2014 .

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