Finite-Time Control Synthesis for Discrete Fuzzy Switched Singularly Perturbed Systems

This brief addresses the synthesis for a class of discrete fuzzy switched singularly perturbed systems (SPSs) in finite time. Different from Lyapunov stability, finite-time stability (FTS) is set up to analyze the transient performance, where the state remains within the upper thresholds for a given finite-time interval. In the face of singular perturbation, a singular-perturbation-parameter-dependent Lyapunov function is firstly introduced for fuzzy switched SPSs in the sense of finite time. Inspired by the mode-dependent average dwell time (MDADT) switching rule, a developed FTS is constructed to eliminate an ill-conditioned issue owing to a singularly perturbed parameter. Furthermore, a new fuzzy control strategy is proposed to satisfy the predefined FTS. Finally, the feasibility of the main results is proved using an inverted pendulum model.