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On minimality in the partial realization problem. (English) Zbl 0626.93009

Given a finite sequence \(M_ 1,...,M_ r\) of \(p\times m\) matrices, a dynamical system \(\Sigma =(A,B,C)\) is called a realization of \(M_ 1,...,M_ r\) if \(CA^{i-1}B=M_ i\) for \(i=1,...,r\). Minimal realizations, that is realizations of the smallest possible state space dimension, are important in many control problems. In this paper, the authors present an algorithm to reduce an arbitrary realization of \(M_ 1,...,M_ r\) to a minimal one. Furthermore a minimality criterion and a formula for the minimal state space dimension are obtained.
Reviewer: A.Perdon

MSC:

93B20 Minimal systems representations
93B15 Realizations from input-output data
93C05 Linear systems in control theory
93B25 Algebraic methods
93B40 Computational methods in systems theory (MSC2010)
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