LMI approach to the mixed H-2/H-infinity filtering design for discrete-time uncertain systems

Abstract

The problem of full-order robust filtering design for discrete-time uncertain linear systems is addressed. The uncertain parameters are assumed to belong to convex bounded domains (polytope type uncertainty), The main purpose is to design a stable linear filter such that the filtering error output signal remains bounded, For that, the parameterization of all linear filters assuring quadratic stability with an H-infinity attenuation constraint to the filtering error system is provided in terms of linear matrix inequalities (LMIs). Then, through the definition of an auxiliary cost, an upper bound to the filtering error variance is minimized, providing a mixed H-2/H-infinity guaranteed cost filtering design, Standard optimization procedures with global convergence assured can be used to solve the problem, as illustrated by an example.