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Research on Robust Control for Nonlinear Fuzzy Time-Delay Systems

Author: LiLi
Tutor: LiuXiaoDong
School: Dalian University of Technology
Course: Control Theory and Control Engineering
Keywords: T-S Fuzzy model Time systems Robust stability Linear matrix inequation(LMI) Uncertainty
Type: PhD thesis
Year: 2008
Downloads: 552
Quote: 4
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As an active research field,the nonlinear systems theory makes a rapid progress recently, which plays an important role in control fields.Fuzzy systems are successfully applied to many control problems because they do not need to accurate mathematical models of the system and can cooperate with human experts’ knowledge.Furthermore,the controller design is easier to be realized in fuzzy control techniques and is stronger robust characteristic.Since 80’s 20th century,the fuzzy control obtains great development in control theory and engineering.It is well known that time delays are frequently encountered in a variety of dynamic systems,and they are often sources of instability and degradation of control performance in control systems. So the study of dynamic control systems with delays is important in both theory and practice, and has thus been of great interest to a large number of researchers for the last few decades. However,researcheres do not pay attention to nonlinear fuzzy time-delaysystems,which is the more general and more complicated system.Accordingly,based on fuzzy control technique,the purpose of this dissertation is to Study robust control and present the more relaxed stability conditions for nonlinear fuzzy time delay systems.For ToS fuzzy systems with state delays,H_∞control problem is considered.A proposed stabilization condition is concise and integral,which overcomes such a drawback that the inter-actions among the time-delay fuzzy subsystems are not considered,and collects the interactions in a single matrix in terms of linear matrix ineqUalities(LMIs).Furthermore,in this paper,with a matrix decoupling technology,the Stability conditions by one step presented is less conserva-tive,which makes the matrix dimensions largely reduced comparing with the matrix dimensions of the two step stability conditions.And the proof is given in detail that the relaxed stability conditions by one step is equivalent to the relaxed stability conditions by two step.Then the designs for the H_∞controller based on fuzzy observers are presented and the condition for the existence of the H_∞controller is given.Finally,an example shows the proposed method is effective.Another point worth mentioning,in the existing papers,the range of time-varying delay considered is from zero to an upper bound.In practice,the range of delay varies in a range for which the lower bound is not restricted to be zero.In this case,the criteria in the previous work are conservative because they do not take into account the information of the lower bound of de-lay.In this paper,some delay-dependent stability criteria are obtained for the T-S fuzzy interval time-varying delay system with nonlinear perturbation.A new Lyapunov-Krasovskii functional is constructed and non-correlated augmented items are used to improve delay-dependent results. Furthermore,nonlinear perturbations assumed both nonlinear time-varying perturbations and time-varying uncertainties in linear fractional form are considered,which makes the fuzzy model general.Compared with the existing results,the methods of this paper is not used free weighting matrices,but also it can lead to the same as the bound of delay with free weighting matrices, even much larger upper of delay.Some numerical examples have shown that the obtained results are less conservative and more flexible.A combination of descriptor model transformation approach and Moon’s integral inequality technique is effective method to deal with the linear time-varying delay systems.In this paper, this methods are extended to research the T-S fuzzy time-varying delay systems.The stability criteria are presented for the T-S fuzzy systems with state delay and input delay.The key features of the approach include a new kind of Lyapunov-Krasovskii functional and a descriptor model transformation with a recent result on bounding of cross products of vectors.Based on this results,H_∞control problem is solved for T-S fuzzy systems with state delays and input delays.The proposed method overcomes the conservation of matrix inequality magnified during the derivation of Lyapunov functional.To obtain the fuzzy controller design,the core complementary linearization algorithm for solving the stabilization problem is given.A series of examples show the proposed delay-dependent stabilization conditions are less conservation than the existing’s results,which make the upper bound of delay larger.It is well known that the traditional isolated control system is going to be replaced by a networked control system(NCS)as the computer network technology is being developed rapidly. And much attention on stability analysis and controller design of NCS is paid.In this paper, a novel control scheme is proposed for the T-S fuzzy system with time-varying delays in a network situation.Utilizing a fuzzy control method and considering the quality of service(QoS) in network systems,the corresponding state feedback control law is obtained.Further,some sufficient conditions and the designs of state feedback controllers are proposed by solving a set of LMIs.A New intrgral inequality approach is used,which makes the results less conservative. The simulations show the proposed method is effective.

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