Realization theory in Hilbert space. (English) Zbl 0668.93018

A representation theorem for infinite-dimensional, linear control systems is proved in the context of strongly continuous semigroups in Hilbert spaces. The result allows for unbounded input and output operators and is used to derive necessary and sufficient conditions for the realizability in a Hilbert space of a time-invariant, causal input-output operator \({\mathcal T}\). The relation between input-output stability and stability of the realization is discussed. In the case of finite-dimensional input and output spaces the boundedness of the output operator is related to the existence of a convolution kernel representing the operator \({\mathcal T}\).


93B15 Realizations from input-output data
93C25 Control/observation systems in abstract spaces
93B25 Algebraic methods
93C05 Linear systems in control theory
93B28 Operator-theoretic methods
93D25 Input-output approaches in control theory
Full Text: DOI


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