Mathematical systems theory

, Volume 21, Issue 1, pp 147–164

Realization theory in Hilbert space

  • Dietmar Salamon

DOI: 10.1007/BF02088011

Cite this article as:
Salamon, D. Math. Systems Theory (1988) 21: 147. doi:10.1007/BF02088011


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 ℐ. 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 ℐ.

Copyright information

© Springer-Verlag New York Inc 1988

Authors and Affiliations

  • Dietmar Salamon
    • 1
  1. 1.Mathematics InstituteUniversity of WarwickCoventryEngland

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