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Robust Control for Uncertain T-S Fuzzy Time-Delay Systems

Author: LiYongMin
Tutor: XuShengYuan
School: Nanjing University of Technology and Engineering
Course: Control Science and Engineering
Keywords: T-S Model Time-Delay Systems Stochastic Systems Robust Control Robust H_∞Control Guaranteed-Cost Control Free-Weighting Matrices LMI Relaxed-LMI
CLC: TP13
Type: PhD thesis
Year: 2008
Downloads: 457
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Abstract


An advantage of a T-S fuzzy model is that,when it is applied to study the system analysis and controller design,one can first represent a nonlinear system as a fuzzy model,and then study the problems of stability and controller design by using a symmetric approach. When time delays,uncertainties and/or stochastic disturbance appear in a T-S fuzzy system, they may affect the system performance seriously,and even make the system unstable. Hence,this dissertation is concerned with the robust control problem of uncertain T-S fuzzy time-delay systems.Based on the previous studies,regarding new problems and using new research methods,some of the robust control problems for uncertain T-S fuzzy time-delay systems are solved.Since the classical LMI technique causes fairly big conservatism in the fuzzy system analysis and control problems,this paper uses two new techniques,namely the freeweighting matrix technique and relaxed LMI approach to reduce the conservatism in system design.Both the continuous-time and discrete-time cases are considered.For the continuoustime T-S fuzzy time-delay system,distributed time delays and input time delays are dealt with by means of the proposed method to show the usefulness of reducing conservatism caused by the ordinary methods.For discrete-time situation,sector time delays,input time delays and stochastic terms are considered using both the two methods to get the stability region of closed-loop systems.A unified framework is established to solve the controller analysis and design problems.The main work of this paper is as follows:Chapter 1:Introduces the history,method and current situation for the study of fuzzy systems,uncertain systems,time-delay systems and stochastic systems.Chapter 2:Here we consider the problems of robust stabilization and robust H_∞control for neutral T-S fuzzy systems with both discrete and distributed delays.It is pointed out that a neutral system obtained by enlarging the dimension of a distributed delay system is not equivalent to the original distributed delay system,and thus the approach in[31]cannot be extended in a straightforward way to the stabilization and H_∞control problems for fuzzy neutral systems with distributed delays.This shows that the generalization from the neutral fuzzy system without distributed delays to that with distributed delays is essential.The provided numerical example also demonstrates the effectiveness of the robust H_∞controller design method.In addition,in order to further reduce the conservatism of the design conditions, we provide another result on the robust H_∞controller design by using the relaxed LMI approach. Chapter 3:Concerned with the guaranteed-cost control problem for neutral T-S fuzzy systems with both discrete and distributed delays based on the free-weighting matrix approach. A sufficient condition for the solvability of this problem is obtained by using a novel Lyapunov functional.This condition,however,is not in the LMI form.By using the matrix transformation techniques,an LMI-based condition for the solvability of the optimal guaranteed-cost control problem is derived and an estimate of the upper bound of the optimal cost is obtained.As a special case,a corollary is given for the guaranteed-cost control problem of linear neutral systems with discrete and distributed delays.It is shown through a numerical example that the proposed results are less conservative than that in[30].Chapter 4:Concerned with the robust stabilization problem for uncertain T-S fuzzy systems with both distributed delays and input delays.It is emphasized that the control input is related to the premise variables when studying the feedback control for T-S fuzzy systems with input delays.Thus,the approaches to linear systems with input delays cannot be extended in a straightforward way to fuzzy systems with input delays.This is the essential difference of the input-delayed fuzzy systems from the input-delayed linear systems.Chapter 5:Concerned with the robust control problem for uncertain discrete-time stochastic T-S fuzzy time-delay systems.The time delays are assumed to take an interval form. Based on the LMI approach,a sufficient condition for the stochastic stabilization of the considered system is obtained.Further,a less conservative result on the same problem is derived by using the relaxed LMI approach.A comparison of the stability region obtained by using the two methods is given.A numerical example is also provided to demonstrate the effectiveness of the proposed design methods.Chapter 6:Investigates the robust H_∞control problem for uncertain discrete-time stochastic T-S fuzzy systems with interval time-varying delays.By applying the free-weighting matrix technique together with the relaxed LMI approach,sufficient conditions for the H_∞performance analysis,controller design and solvability of the problem are given in a unified framework.Chapter 7:Concerned with the robust control problem for uncertain discrete-time stochastic T-S fuzzy systems with input delays.Since the stochastic terms are considered,the approach developed in this chapter is different from the one in Chapter 3.Moreover,we divide the controller design and the solution into two steps,and then complete the stabilization in a unified framework.This is different from Chapter 5.Finally,a numerical example is provided to demonstrate the effectiveness of the proposed design method.Chapter 8:Concludes the thesis and points out some open problems that should be further studied.

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