Synthesis of a Dynamical Output ${H}_{\infty}$ Controller for the Fuzzy Input-Output Model

Abstract

In this paper, the issue of dynamical output ${H} _{\infty }$ controller designing is addressed for the fuzzy input-output (FIO) model. The FIO model is significantly distinctive from the conventional Mamdani and T-S or T-S-K fuzzy models and can be conveniently used to describe more complicated dynamical systems that cannot be easily handled by the conventional fuzzy models. By using the robust control theory available for both the linear and fuzzy systems, sufficient conditions in terms of the linear matrix inequalities (LMIs) are derived to synthesize a dynamical output feedback ${H} _{\infty }$ controller for the FIO plant. These LMI conditions can be numerically and efficiently solved by the existing convex optimization software, e.g., the MATALB LMI toolbox. Moreover, a motor-spring-mass system abstracted from the real applications is provided to validate the applicability and efficiency of our method.