An improved approach to fuzzy dynamic output feedback H_∞ control of continuous-time Takagi–Sugeno fuzzy systems

Abstract

This paper studies the problem of dynamic output feedback $ H_{\infty } $ H∞ control for continuous-time Takagi–Sugeno fuzzy systems. Based on the fuzzy Lyapunov functions without the special structure, a controller design method is developed and the relaxed stabilisation conditions are proposed. First, some shortcomings of the existing results are improved and a new approach is proposed for bounding the time derivatives of the membership functions. Then, less conservative conditions are obtained by introducing regulable parameters and applying the matrix decoupling techniques, which guarantee the prescribed $ H_{\infty } $ H∞ performance. Moreover, the relaxation technique proposed in this paper is also suitable for the fuzzy system with immeasurable premise variables. Finally, some examples are provided to demonstrate the validity of the approach.