Observer-Based Control for Markovian Jump Fuzzy Systems Under Mismatched Fuzzy Basis Functions

Abstract

This paper investigates the observer-based dissipative control problem for a class of discrete-time Markovian jump fuzzy systems under mismatched fuzzy basis functions. In the practical implementation of the observer-based control scheme, the system state variable can be measured with uncertainties and disturbances, which acts as a factor that prevents accurate measurement of the premise variable. Thus, in this case, it is necessary to explore the phenomenon that the system premise variable cannot be reflected in the design of the fuzzy-basis-dependent observer and controller. In response to this need, this paper proposes a method to deal with the mismatch phenomenon in the observer-based stabilization problem of MJFSs by devising a two-step approach to solve the inherent decoupling problem and by providing a useful relaxation technique for the error of mismatched fuzzy basis functions.