Suboptimal H∞ Filtering via Linear Matrix Inequalities

Abstract Necessary and sufficient conditions are derived for the existence of a solution to the continuous-time and discrete-time reduced-order suboptimal H∞ filtering problems. These conditions are expressed in terms of Linear Matrix Inequalities (LMIs) and a coupling non-convex matrix rank constraint set. In addition, an explicit parametrization of all reduced-order filters that correspond to a feasible solution are provided in terms of a contractive matrix. Computational issues are discussed and an iterative procedure is proposed to solve the reduced-order H∞ filtering problem using alternating projections, although global convergence of the algorithm is not guaranteed.

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