Robust finite-time estimation of Markovian jumping systems with bounded transition probabilities

This paper studies the finite-time state estimation and H∞ filter design problem for a class of uncertain Markovian jumping systems (MJSs) with bounded transition probabilities. Based on the selected Lyapunov–Krasovskii functional, the finite-time H∞ filter is constructed to derive a sufficient condition such that the filtering error dynamic MJSs are finite-time bounded and satisfies a prescribed level of H∞ disturbance attenuation in a finite time-interval. Then, in terms of linear matrix inequalities (LMIs) techniques, the sufficient condition on the existence of finite-time H∞ filter is presented and proved. The filter matrices can be solved directly by using the existing LMIs optimization techniques. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design approach.