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

Author(s):

F.A. Cuzzola, A. Ferrante
Conference/Journal:

vol. AUT01-05
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:

(04)Technical Report
Supervisor:



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% Autogenerated BibTeX entry
@TechReport { CuzFer:2001:IFA_379,
    author={F.A. Cuzzola and A. Ferrante},
    title={{Explicit formulas for LMI-based $H_2$ filtering and
	  deconvolution}},
    institution={},
    year={2001},
    number={},
    address={},
    url={http://control.ee.ethz.ch/index.cgi?page=publications;action=details;id=379}
}
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