Probabilistic dynamic event-based finite-time sliding mode security control for discrete-time singular semi-Markov jump LPV systems

This paper mainly addresses the finite-time sliding mode control (SMC) for discrete-time singular semi-Markov jump linear parameter-varying (SS-MJLPV) systems considering deception attacks and actuator failures. Firstly, to reduce the communication load over the network, a probabilistic dynamic event-triggered protocol (PDETP) is proposed. Secondly, during the process of data transmissions and system operations, it is inevitable that the attackers will maliciously carry out cyber-attacks and the actuators may malfunction, so the occurrences of cyber-attacks and actuator failures are considered in this paper. Then, a suitable sliding surface function and SMC law are developed. Through reachability analysis, the given SMC law can pull the system trajectories onto the designed sliding surface within a specified interval. Additionally, the parameter-dependent asynchronous sliding mode controller based on the hidden Markov model (HMM) is designed to describe the relationship between system modes and controller modes. Furthermore, the parameter-dependent Lyapunov–Krasovskii functional is constructed to demonstrate the singular finite-time boundedness (SFTB) of the SS-MJLPV system and derive the sufficient conditions for both the reaching phase and the sliding motion phase. Finally, a practical example is provided to validate the theoretical results.