Observer-based sliding mode control of discrete-time delayed singular semi-Markov jump systems with random false data injection attacks

The stochastic admissibility of discrete-time delayed singular semi-Markov jump systems is researched in this paper. We consider time delay, extraneous disturbances, and randomly occurring false data injection attacks. The semi-Markov kernel method is performed to analyze the stochastic admissibility of the augmented system, and sufficiency criteria for facilitating numerical detection are established. The new class of Lyapunov functions introduced in the stability analysis relies on the current mode, the delayed mode, and the moment that the last mode switch occurred. A common sliding surface is conceived and its reachability is ensured. Finally, The expected effect of this proposed scheme is demonstrated with a simulation example.