Parameter-dependent filter design with guaranteed ℋ∞ performance

Abstract

In the paper, the problem of ℋ_∞ filtering for a class of linear uncertain systems is studied. The parameter uncertainties are assumed to reside in a polytope. The paper is focused on the design of a parameter-dependent filter which guarantees the filtering error system to be asymptotically stable and has a prescribed ℋ_∞ performance. By employing a parameter-dependent Lyapunov function approach, sufficient conditions are established for the existence of the desired filters in terms of linear matrix inequalities, which can be handled easily by using the available toolbox. Both continuous- and discrete-time cases are investigated. It is shown, via a numerical example, that the proposed filter design methods are more effective and less conservative than some existing results.