Guaranteed Cost Control for Interval Type-2 Fuzzy Semi-Markov Switching Systems Within a Finite-Time Interval

Abstract

This article focuses on the finite-time guaranteed cost (FTGC) control problem for interval type-2 (IT2) fuzzy semi-Markov switching systems (S-MSSs) with additive disturbances. Based on the IT2 fuzzy S-MSSs and the state feedback control method, a novel IT2 mode-dependent fuzzy guaranteed cost (GC) controller is developed under the mismatched membership functions. Then, some new sufficient conditions are given to ensure that IT2 fuzzy S-MSSs are finite-time (FT) stochastically stable based on the designed IT2 mode-dependent fuzzy GC controller. Furthermore, the transition rate boundary condition is relaxed, and a new incomplete transition rate boundary model is constructed to reflect the transition rate information. For both the incomplete transition rate boundaries and the actuator fault phenomenon, the improved stability criteria are provided to stabilize the IT2 fuzzy S-MSSs within an FT interval and determine the gains of the IT2 mode-dependent fuzzy GC controller, resulting in a much greater design flexibility. Distinct from the existing results, the presented FTGC control scheme is more suitable for many practical systems because the IT2 fuzzy S-MSS model, which is more general compared with the traditional fuzzy system and S-MSSs, is considered. Finally, three illustrative examples are offered to explain the effectiveness and feasibility of the proposed FTGC control approach.