Passivity-Based Control of Fuzzy Singularly Perturbed Jump Systems Based on Semi-Markov Kernel Approach

This article investigates the passivity-based fuzzy control problem for discrete-time nonlinear semi-Markov jump singularly perturbed systems (SPSs) by the semi-Markov kernel (SMK) approach. Due to the fact that the statistical information of SMK is difficult to acquire completely, the generally partially available case, covering the completely available and completely unavailable cases, is considered to remove the ideal assumption that the system information is invariably available to controllers. Additionally, the mode-dependent fuzzy rules describing nonlinear behavior are constructed, that is, the membership functions are dependent on the system modes, thus promoting the previous results efficacious in a more accurate form. Subsequently, by fully utilizing available SMK information, some sufficient conditions based on the slow state feedback technique are derived to ensure that the semi-Markov jump fuzzy SPSs are stabilized and satisfy the given passive performance. Finally, the superiority and practicability of the presented theoretical results are explained by a numerical example and an inverted pendulum model.