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Analysis And Synthesis For Time-delayed Fuzzy Systems Via Delay-product-type Functional Method

Posted on:2024-05-23Degree:DoctorType:Dissertation
Country:ChinaCandidate:Z LianFull Text:PDF
GTID:1528307148483474Subject:Control Science and Engineering
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The Takagi-Sugeno fuzzy model can represent a complex nonlinear system as a weighted sum of a set of simple linear subsystems;therefore,the entire nonlinear system can be viewed as a fuzzy approximation of multiple local linear systems.Owing to the good semi-linearization property of the Takagi-Sugeno fuzzy model,the well-established linear control method can be applied to the control problem of nonlinear systems.In addition,time delay is inevitable in most dynamic systems,such as agricultural system and industrial systems.The presence of time delay can degrade the control performance of the system and even lead to system instability.Therefore,the analysis and design problems of time-delay systems have received much attention from scholars in recent decades.The control problems of Takagi-Sugeno fuzzy-model-based nonlinear systems with time delays are not only of crucial theoretical research significance but also significant applied research value.This dissertation investigates the problems of stability,stabilization,robust control and robust filter for Takagi-Sugeno fuzzy-model-based nonlinear systems with time delays using the delay-product-type functional method,integral inequalities and reciprocally convex matrix inequality.The research contents of this dissertation are summarized as follows:(1)Propose stability criteria for time-delayed fuzzy systems based on delay-producttype functional.Based on the Lyapunov-Krasovskii functional method,this dissertation proposes delay-dependent stability criteria for Takagi-Sugeno fuzzy systems with time-varying delays by introducing delay-product-type non-integral terms to construct a novel delayproduct-type Lyapunov-Krasovskii functional using Wirtinger-based integral inequality and extended reciprocally convex matrix inequality to deal with the established functional and its derivation.The introduction of the delay-product-type non-integral terms makes the established Lyapunov-Krasovskii functional contain more useful information on time delays and system states.It helps to derive a more relaxed positive definite condition of the Lyapunov-Krasovskii functional,which can reduce the conservativeness of the obtained stability criterion effectively.(2)Propose a stabilization method for time-delayed fuzzy systems based on improved delay-product-type functional.Based on a parallel distributed compensation control strategy,this dissertation studies the design problem of memoryless state feedback fuzzy controller and proposes delay-dependent stabilization conditions for a class of Takagi-Sugeno fuzzy systems with time-varying delays.An improved delay-product-type Lyapunov-Krasovskii functional is constructed by introducing both delay-product-type non-integral and integral terms,which makes the established Lyapunov-Krasovskii functional contain more useful information on time delays and system states with an appropriate increase in computational complexity.In addition,the Wirtinger-based integral inequality and extended reciprocally convex matrix inequality are utilized to deal with the established functional and its derivation,which effectively improves the control performance of the proposed state feedback fuzzy controller.(3)Propose robust control method for Takagi-Sugeno fuzzy systems with input and state time-varying delays base on improved delay-product-type functional.Considering the existence of parameter uncertainties and external disturbances,this dissertation proposes robust control method for Takagi-Sugeno fuzzy systems with input and state time-varying delays.Specifically,based on delay-product-type functional and multiple integral functional methods,an improved Lyapunov-Krasovskii functional,which contains more helpful information of delays and systems,is constructed by introducing both delay-product-type non-integral and integral terms and triple integral terms.The performance is analyzed using the Wirtinger-based integral inequality,Jensen integral inequality and extended reciprocally convex matrix inequality.Then,by making use of the input delay and using a parallel distributed compensation control strategy with parameter regulation method and matrix decoupling techniques,the memory state feedback fuzzy controller is designed that ensures the closed loop system is asymptotically stable with a prescribed performance level.(4)Propose piecewise fuzzy filter method for fuzzy-affine systems with time delays based on fuzzy-dependent delay-product-type functional.Based on the Takagi-Sugeno fuzzy-affine model,this dissertation proposes a piecewise fuzzy filter method for fuzzy-affine systems with time delays and energybounded random disturbances.Specifically,based on the piecewise,fuzzy-dependent,and delay-product-type functional methods,a fuzzy-dependent delay-product-type Lyapunov-Krasovskii functional is constructed by introducing the information and membership function and delay-product-type terms.The performance is analyzed using the Wirtinger-based integral inequality,S-procedure and extended reciprocally convex matrix inequality.Then,by applying matrix inequality linearization techniques,the piecewise fuzzy filter is designed that ensures the closed loop system is asymptotically stable with a prescribed performance level.
Keywords/Search Tags:Time-delay systems, Takagi-Sugeno fuzzy systems, Robust control, Lyapunov-Krasovskii functional, Integral inequality
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