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Constrained controllability of linear retarded dynamical systems. (English) Zbl 0797.93004

Summary: The main purpose of the paper is to study the constrained controllability for linear, time-invariant dynamical systems defined in infinite- dimensional Banach or Hilbert spaces. First the brief theory of such dynamical systems is recalled. Next, different definitions of controllability are presented and the relationships between them are explained. Using the general spectral theory of unbounded linear operators, many constrained controllability conditions are formulated and proved. Finally, a simple illustrative example is given. The results presented extend to the case of abstract retarded dynamical systems, constrained controllability conditions given in the literature for finite-dimensional case or systems without delays.

MSC:

93B05 Controllability
93C05 Linear systems in control theory
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