Reserach ArticleFinite-time H∞ control for a class of Markovian jump systems with mode-dependent time-varying delays via new Lyapunov functionals

- A less conservative condition is developed based on new Lyapunov functionals and free weighting matrices.
- In order to reduce the conservatism, a new method has been proposed to deal with term −∫−h0∫t+θtẋ⊤Ziẋdsdθ.
- A novel sufficient condition for finite-time stability of H∞ control is derived and the system trajectory stays within a prescribed bound.
- Two examples are provided to show the benefit of the proposed method.

This paper is concerned with the problem of finite-time H∞ control for a class of Markovian jump systems with mode-dependent time-varying delays via new Lyapunov functionals. In order to reduce conservatism, a new Lyapunov-Krasovskii functional is constructed. Based on the derived condition, the reliable H∞ control problem is solved, and the system trajectory stays within a prescribed bound during a specified time interval. Finally, numerical examples are given to demonstrate the proposed approach is more effective than some existing ones.