Completely J —positive linear systems of finite order |
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Authors: | Aurelian Gheondea Raimund J Ober |
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Abstract: | Completely J — positive linear systems of finite order are introduced as a generalization of completely symmetric linear systems. To any completely J — positive linear system of finite order there is associated a defining measure with respect to which the transfer function has a certain integral representation. It is proved that these systems are asymptotically stable. The observability and reachability operators obey a certain duality rule and the number of negative squares of the Hankel operator is estimated. The Hankel operator is bounded if and only if a certain measure associated with the defining measure is of Carleson type. We prove that a real symmetric operator valued function which is analytic outside the unit disk has a realization with a completely J — symmetric linear space which is reachable, observable and parbalanced. Uniqueness and spectral minimality of the completely J — symmetric realizations are discussed. |
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Keywords: | Discrete time linear system sign symmetry asymptotic stability Kreǐ n space definitizable operator completely J — positive linear system of finite order defining measure realization theory spectral minimality |
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