Robust H∞ filters for uncertain discrete-time stochastic systems

This paper is concerned with the robust H_∞ filtering for uncertain discrete-time stochastic systems with polytopic uncertainties. To solve this problem we introduce same slack matrix variables and then use a polynomial parameter dependent approach. Then some conditions expressed as strict linear matrix inequality conditions are derived, which can be easily tested by using standard numerical software. This new approach is shown, via a numerical example, to be less conservative than previous results in the quadratic and parameter-dependent frameworks.