Resilient L2‐L∞ Filtering of Uncertain Markovian Jumping Systems within the Finite‐Time Interval

This paper studies the resilient L2‐L∞ 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 L2‐L∞ 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 L2‐L∞ 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 L2‐L∞ 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.