Dual switching dynamic event-triggered controls of stochastic Takagi–Sugeno fuzzy semi-Markov jump systems

In this paper, the stability analysis for a class of stochastic nonlinear Takagi–Sugeno fuzzy semi-Markov jump systems (TSFS-MJSs) is studied under a novel dual switching dynamic event-triggered fuzzy controller. Unlike conventional deterministic or stochastic systems governed by event-triggered controllers, the constructed controller strategy contains primary control and auxiliary control, enabling the controller to switch between these dual controls. Besides, the novel dual switching dynamic event-triggering mechanism (DSD-ETM) is founded on state detection, condition analysis, and switching signal of TSFS-MJSs, ensuring that the operation of the controller is entirely dictated by the DSD-ETM. In addition, the DSD-ETM allows for the avoidance of the Zeno phenomenon and directly obtains the minimum inter-execution time across different subsystems within TSFS-MJSs. Based on an augmented Lyapunov function with mode-dependent, the sufficient conditions for the mean-square asymptotic stability and the mean-square exponential stability of TSFS-MJSs with dual switching dynamic event-triggered fuzzy controller are obtained. Finally, an application example involving a nonlinear double-link robot arm model is presented to illustrate and validate our results.