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

作者：Li, Mengling^*; Deng, Feiqi; Zheng, Xiaofeng; Luo, Jinnan

来源：JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2021, 358(2): 1291-1307.

DOI：10.1016/j.jfranklin.2020.11.025

• DELAY-DIFFERENTIAL EQUATIONS
• MODEL

This paper is concerned with the mean-square asymptotic stability of stochastic system with Markovian switching and Levy 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 Levy 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.

• 单位
  佛山科学技术学院; 电子科技大学