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Balanced parametrization of classes of linear systems. (English) Zbl 0741.93010
The objective of the paper is to show that for many classes of linear systems it is possible to derive canonical forms (realizations) using the idea of balancing. The general principle of balancing is to associate with a particular class of systems a set of Riccati equations that are intrinsically related with the properties of the particular class of systems. The class of asymptotically stable systems is, e.g., associated with a set of Lyapunov equations, whereas the set of positive real systems is associated with the positive real Riccati equations. It is shown that by imposing further constraints on the realization, it is possible to obtain a unique realization, i.e. a canonical form. Applications of these results to Hankel operators and model reduction are discussed.

MSC:
93B10 Canonical structure
93C05 Linear systems in control theory
93B20 Minimal systems representations
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