Almost sure synchronization of T-S fuzzy semi-Markov asynchronous switched systems under deception attacks

This paper investigates almost sure synchronization of T-S fuzzy semi-Markov asynchronous switched systems under deception attacks. In the considered system, the mode transitions follow a semi-Markov process with generally distributed sojourn times, while deception attacks occur at stochastic discrete time instants, independent of the system’s switching process. First, the deception attack is modeled as a renewal-driven stochastic impulsive process, where the attack occurrence times follow a renewal process and the attack intensities vary randomly. Then, by constructing a mode-dependent Lyapunov function and utilizing the strong law of large numbers, sufficient conditions for almost sure synchronization are derived. Compared with existing studies, our work models the asynchrony between semi-Markov switching and deception attacks, leading to a more general and realistic framework for analyzing complex networked systems under adversarial conditions. Finally, numerical simulations on an oscillator model are conducted to validate the effectiveness of the proposed method.