Robust H-infinite Filtering Problem On T-S Fuzzy Time-delay Systems

Nonlinearity, time delay and uncertainty are common physical phenomena in the natural world, and it is of great significance to our life through studying these phenomena. Fuzzy systems could offer an effective method to control the complex systems, bad systems or uncertain systems by using experts’ knowledge. The T-S fuzzy model, first proposed by Takagi and Sugeno in 1985, is able to approximate any smooth nonlinear function to any specified accuracy with any compact set, in which a nonlinear system is transformed into a set of linear subsystems, thus we can solve nonlinear problems employing the well-established theory and tools of linear systems. Therefore, T-S fuzzy system as a tool to deal with nonlinear problems has attracted more and more attention.In this article, we will discuss and research in the following aspects:(1) The basic knowledge of fuzzy logic systems is introduced, and usual types, emergence and development of fuzzy control have been also introduced. Further, T-S fuzzy systems are presented. Lastly, the related knowledge of linear matrix inequality(LMI) has been summarized.(2) The decades of development on robust filtering theory has been simply elaborated. In addition, the basic knowledge of stability theory is presented and several kinds of models about stability problems have been researched.(3) The H-infinite filtering problem of nonlinear T-S fuzzy systems with time-varying delay is investigated. Then, the asymptotically stable sufficient conditions for H-infinity filtering system are proposed and small conservative results are obtained.(4) Further, an improved H-infinite filtering problem of nonlinear T-S fuzzy systems with time-varying delay is studied and relevant Lemmas are presented. Moreover, less conservative results are presented ensuring system stability and H-infinite filter performance indicators.(5) Based on the existing related theory of nonlinear T-S fuzzy systems with time-varying delay, nonlinear H-infinite filter problem with uncertainty is also discussed.The innovation of the paper is as follows:Against with robust H-infinite filtering problem of nonlinear T-S fuzzy systems with time-varying delay, some of the formulas during derivation of a function are often omitted, which leads to a large conservative result. This paper doesn’t adopt the conventional method, none of the items during derivation of a function is neglected. The related theory methods and good results are obtained by combining with convex optimization approach, introducing liberty matrix variables, using LMI techniques and Schur complement method, which greatly reduces the conservativeness of the system. Finally, comparing with the references, this method has obvious advantages.In the end, we conclude the text and point out some problems that would be studied further.