Robust H∞ filtering for uncertainty delay systems

This paper is concerned with the problem of the robust H_∞ filtering for uncertainty systems with time delay. The uncertainty is assumed to be of polytopic type. A delay-dependent linear matrix inequality method is presented based on a Lyapunov-Krasovskii functional and the algorithm of filter design is given. The key features of the approach include the introduction of free-weighting matrices and model transformation. The parameterized model transformation method expresses the delay term in terms of an integral, and free weighting matrices method expresses the relationships between the terms in the Leibniz-Newton formula. The free weighting matrices method overcomes the conservativeness of methods involving a fixed model transformation. Numerical examples are given to show the less conservativeness of the results.