$H_{\infty }$ Observer Design for Fuzzy System With Immeasurable State Variables via a New Lyapunov Function

This paper is concerned with the design of H
_∞
observers for fuzzy system with immeasurable state variables via a new Lyapunov function. By decomposing the space of premise variables into crisp regions and fuzzy regions, piecewise fuzzy H
_∞
observers are established at different instants to cope with the challenges caused by the mismatch of the premise variables and exogenous disturbances. Based on the proposed new Lyapunov functions that depend on the different regions where the premise variables are located, sufficient conditions in terms of linear matrix inequalities are obtained to guarantee the stability and desired performance of the error systems. Finally, a simulation example is provided to show that the new design technology proposed in this paper achieves better H
_∞
performance than the existing design methods.