Asynchronous observer-based finite-time control for nonlinear Markovian jump systems with time-varying delays

This paper addresses the problem of finite-time observer-based control for continuous-time nonlinear Markovian jump systems with time-varying delays. The existing studies about asynchronous observer-based control for Markovian jump systems in continuous-time case only consider the asynchronism of controller and original system, but suppose that the observer and original system are switched with the same Markovian process, which is unreasonable in practice. In this paper, the modes of observer and controller are supposed to be asynchronous with the modes of original system simultaneously. Firstly, by constructing novel Lyapunov–Krasovskii functionals and using finite-time analysis theory, the error system is proved to be finite-time bounded with an $$H_\infty $$ performance level. Secondly, the parameters of desired observer and controller are calculated by virtue of linear matrix inequalities. Finally, two numerical examples are provided to illustrate the less conservativeness and effectiveness of our proposed method.