Mean-square stability of stochastic system with Markov jump and Lévy noise via adaptive control

This paper is concerned with the mean-square asymptotic stability of stochastic system with Markovian switching and Lévy noise by adaptive control method. Firstly, a class of general systems is considered and the information including the bounds of the nonlinear parameters and external disturbance is unavailable. Then an adaptive controller is designed to achieve the scheduled goal by utilizing Lyapunov function and M-matrix method. Next, a class of Markov jump linear systems which suffers unknown external disturbance and Lévy noise is discussed, the corresponding adaptive controller can force the state trajectories of the systems to achieve mean-square asymptotic stability. Finally, two theoretical examples and a practical example are provided to explain the validity of the presented results.