Realization theory in Hilbert space. (English) Zbl 0668.93018

Salamon, Dietmar

Math. Syst. Theory 21, No. 3, 147-164 (1988).

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 \({\mathcal T}\).

MSC:

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

Keywords:

strongly continuous semigroups in Hilbert spaces; input-output stability; convolution kernel; time-invariant

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