Resilient L 2 - L ∞ Filtering of Uncertain Markovian Jumping Systems within the Finite-Time Interval

Abstract

This paper studies the resilient $L_2$-$L_{\infty }$ filtering problem for a class of uncertain Markovian jumping systems within the finite-time interval. The objective is to design such a resilient filter that the finite-time $L_2$-$L_{\infty }$ gain from the unknown input to an estimation error is minimized or guaranteed to be less than or equal to a prescribed value. Based on the selected Lyapunov-Krasovskii functional, sufficient conditions are obtained for the existence of the desired resilient $L_2$-$L_{\infty }$ filter which also guarantees the stochastic finite-time boundedness of the filtering error dynamic systems. In terms of linear matrix inequalities (LMIs) techniques, the sufficient condition on the existence of finite-time resilient $L_2$-$L_{\infty }$ filter is presented and proved. The filter matrices can be solved directly by using the existing LMIs optimization techniques. A numerical example is given at last to illustrate the effectiveness of the proposed approach.