Adaptive fault-tolerant double asynchronous control for switched semi-Markov jump systems via improved memory sampled-data technique

In this article, the issue of adaptive fault-tolerant (AFT) double asynchronous control for a category of switched semi-Markov jump systems (SSMJSs) is studied. Ground on the average dwell time (ADT) mechanism, a high-level switching signal is designed to adjust the change of the low-level semi-Markov chain. For two different switching rules, the double asynchronous phenomenon from the system to the controller is considered, namely, the asynchronous issue of low-level Markov jump modes and the mismatched switching when the high-level switching signals occur in the sampling interval. In addition, a new nonlinear AFT control method is proposed, which is more general than the traditional fault-tolerant model. Besides, an improved double-sided looped -functional method is constructed for sampled-data control (SDC), such that the selected Lyapunov-Krasovskii functional (LKF) can include two novel time-integral states. By using integral inequalities, the sufficient conditions for the system to be exponentially stable are obtained. In the end, the feasibility of the results is proved by comparing the results with some existing approaches through two examples.