Brief Explicit formulas for LMI-based H2 filtering and deconvolution

Authors:
Francesco A. Cuzzola;Augusto Ferrante
Affiliations:
Dipartimento di Elettronica e Informazione-Politecnico di Milano, P.za L. da Vinci 32, 20133 Milano, Italy;Dipartimento di Elettronica e Informazione-Politecnico di Milano, P.za L. da Vinci 32, 20133 Milano, Italy
Venue:
Automatica (Journal of IFAC)
Year:
2001

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Abstract

This paper is concerned with the H"2-optimal estimation of a linear combination of the state and of the input of a discrete-time linear time-invariant dynamic system. We reformulate such problem in terms of a set of three linear matrix inequalities (LMI) and we provide explicit formulas to compute a family of solutions for such LMIs. This family is explicitly parameterized by a real parameter @e. The H"2 performance of the corresponding filter may be rendered arbitrarily close to the optimum by choosing a sufficiently small @e. This procedure is shown to be computationally very efficient.