Abstract
This paper gives a new systematic framework to solve the asynchronous sliding mode control (SMC) problem for the semi-Markovian jump systems with singular perturbations, which can effectively remove the dependence on the unavailable system mode of SMC controller in some existing works. By considering the effect of the singular perturbation, this paper introduces a novel ε-dependent common sliding function, and then an asynchronous SMC law is developed by just using the detected mode signal. In order to overcome the difficulties in analyzing the stability of the sliding mode dynamics and the reachability of the specified sliding surface, a novel matrix decoupling technique and a novel semi-Markovian Lyapunov function method are introduced. Besides, genetic algorithm (GA) is employed to solve two meaningful optimization problems arising from designing a desired asynchronous SMC scheme. Finally, an operational amplifier circuit with a switching positive temperature coefficient thermistor is simulated to show the practicability of the proposed asynchronous SMC approach via GA.
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