A generalized parameter-dependent approach to robust H∞ filtering of stochastic systems

This paper is concerned with the problem of robust H ∞ filtering for discrete-time stochastic systems with state-dependent stochastic noises and deterministic polytopic parameter uncertainties. We utilize the polynomial parameter-dependent approach to solve the robust H ∞ filtering problem, and the proposed approach includes results in the quadratic framework that entail fixed matrices for the entire uncertain domain and results in the linearly parameter-dependent framework that use linear convex combinations of matrices as special cases. New linear matrix inequality (LMI) conditions obtained for the existence of admissible filters are developed based on homogeneous polynomial parameter-dependent matrices of arbitrary degree. As the degree grows, a test of increasing precision is obtained, providing less conservative filter designs. A numerical example is provided to illustrate the effectiveness and advantages of the filter design methods proposed in this paper. © Birkhäuser Boston 2008