Robust H_∞ filtering for Markov jump systems with interval time-varying delay

This paper investigates the problem of robust H_∞ filtering for linear Markov jump systems with interval time-varying delay. Different from conventional techniques dealing with various delay dependent conditions for time-delay systems, a precise upper estimation is presented for a combination of positive-definite matrices with reciprocal coefficients. By proposing this method, a novel sufficient condition for the solvability of the Markov jump linear filter is obtained, which guarantees stochastic stability and a prescribed H_∞ disturbance attenuation level of the resulting filtering error system. And the desired filter can be constructed by solving a set of LMIs. An illustrative example is provided to demonstrate the effectiveness of the proposed method.