Analysis And Design Of H? Filtering Based On Discrete TS Fuzzy Systems With Time-varying Delays

Nonlinearity and time delay are common and inevitable physical phenomena in control systems,and they are also one of the hotspots and difficulties in control theory research.Because the Takagi-Sugeno fuzzy model has the property of infinitely approximating any continuous function in a closed bounded domain,that is,a complex nonlinear system can be transformed into a linear system,and the existing linear theory and tools can be used for analysis and synthesis.It provides an effective control method for dealing with complex systems and systems containing various uncertain problems.Therefore,the analysis and synthesis of T-S fuzzy systems with delay-dependent has important theoretical and practical significance,which has attracted widespread attention from many scholars.This paper is devoted to the analysis and design of H?filtering for discrete-time T-S fuzzy systems with time-varying delays.Due to the common boundary inequalities have limitations in dealing with the quadratic accumulation terms in Lyapunov-Krasovskii function and the results obtained are more conservative.Based on previous research,this paper analyzes and compares the Free-weighting matrix method,Jensen's inequality and Wirtinger-based inequality with the newly proposed Wirtinger-based inequality with quadratic summation term and reciprocally convex approach.The idea of delay-partitioning and the method of relaxing the positive definite condition of Lyapunov matrix are analyzed and studied.Firstly,for a delay-dependent discrete-time linear system,the problems of H?filtering for discrete-time system with time-varying delay is researched.By introducing appropriate Lyapunov-Krasovskii functional,and combining with Wirtinger-based inequality with quadratic summation term,the two bounded real lemmas of discrete-time linear systems with time delay are obtained,respectively.Then,the H? filter design method for discrete-time systems with time-delay based on LMIs is proposed by using the contract matrix transformation method,and the numerical analysis results show that the proposed filter design method is less conservative than the existing methods in the literature.Secondly,for a delay-dependent discrete-time T-S fuzzy system,based on the proposed bounded real lemma,combined with the delay-partitioning idea,an appropriate Lyapunov-Krasovskii functional,and Wirtinger-based inequality with quadratic summation term,to study the H? filtering design of discrete-time T-S fuzzy systems with time-varying delay.Thus,utilizing the contract matrix transformation method,a H? filter design for discrete-time T-S fuzzy systems with time-varying delay based on linear matrix inequality is proposed.Next,a few numerical analysis results are given to prove the effectiveness of the method.Finally,the proposed method has been improved.Based on the previous research,the positive definite conditions for the Lyapunov matrix are relaxed,and the H? filtering problem of discrete-time T-S fuzzy systems with time-varying delays is considered.Then,a H? filter design method for discrete-time T-S fuzzy systems with time-varying delay based on LMI is proposed.Also,some numerical simulations are given to prove that this method can further reduce the conservativeness of the results obtained.