Robust energy-to-peak filtering for Markov systems with interval time-delay

The energy-to-peak filtering problem of Markov jump systems with interval time-varying delay is investigated in this note. The proposed method in dealing with time-delay incorporates a mode-dependent Lyapunov functional and a precise upper estimation for a combination of positive-definite matrices with reciprocal coefficients. A novel sufficient condition for the solvability of the desired mode-dependent filter can be constructed by solving a set of standard LMIs, which guarantees stochastic stability and a prescribed l₂-l_∞ disturbance attenuation level of the resulting filtering error system. An illustrative example is provided to demonstrate the effectiveness of the proposed method.