# Explicit formulas for LMI-based $H_2$ filtering and deconvolution

Author(s):F.A. Cuzzola, A. Ferrante |
Conference/Journal:Automatica, vol. 37, no. 9, pp. 1443-1449 |

Abstract:This paper is concerned with a very general version of the unbiased filtering problem in an $H_2$ framework. More precisely, we consider 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 a linear algebraic framework in terms of a set of three Linear Matrix Inequalities (LMI) and we provide explicit formulas to compute a family of solutions for such LMI's. This family is explicitly parameterized by a real parameter $varepsilon$. The $H_2$ performance of the corresponding filter may be rendered arbitrarily close to the optimum by choosing a sufficiently small $varepsilon$. This procedure avoids convex optimization algorithms which can be computationally demanding and does not require assumptions on the system dynamics. | Year:2001 |

Type of Publication:(01)Article | |

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% Autogenerated BibTeX entry @Article { CuzFer:2001:IFA_250, author={F.A. Cuzzola and A. Ferrante}, title={{Explicit formulas for LMI-based $H_2$ filtering and deconvolution}}, journal={Automatica}, year={2001}, volume={37}, number={9}, pages={1443--1449}, month=sep, url={http://control.ee.ethz.ch/index.cgi?page=publications;action=details;id=250} } | |

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