Stability analysis and security control of nonlinear singular semi-Markov jump systems

This paper mainly studied the stochastic stability and the design of state feedback controllers for nonlinear singular continuous semi-Markov jump systems under false data injection attacks. Based on the Lyapunov function and the implicit function theorem, a basic stochastic stability condition of the system was given to ensure that the nonlinear singular semi-Markov jump system under attack was regular, impulse-free, unique, and stochastically stable. On this basis, the stochastic admissible linear matrix inequality conditions of the system were obtained by using the singular value decomposition of the matrix and Schur's complement lemma. To design the state feedback controller, based on the upper and lower bounds of the time-varying transition probability of the semi-Markov jump system and the singular value decomposition method, the stochastic stable linear matrix inequality condition of the closed-loop system under the false data injection attack was established. Finally, the validity and feasibility of the results were verified by numerical examples.