Delay-Dependent Finite-Time H∞ Filtering for Markovian Jump Systems with Different System Modes

Abstract

This paper is concerned with the problem of delay-dependent finite-time $H_{\infty }$ filtering for Markovian jump systems with different system modes. By using the new augmented multiple mode-dependent Lyapunov-Krasovskii functional and employing the proposed integrals inequalities in the derivation of our results, a novel sufficient condition for finite-time boundness with an $H_{\infty }$ performance index is derived. Particularly, two different Markov processes have been considered for modeling the randomness of system matrix and the state delay. Based on the derived condition, the $H_{\infty }$ filtering problem is solved, and an explicit expression of the desired filter is also given; the system trajectory stays within a prescribed bound during a specified time interval. Finally, a numerical example is given to illustrate the effectiveness and the potential of the proposed techniques.