
doi: 10.1137/0316041
Controllability of linear retarded systems is investigated by using the abstract representation of such systems given by $\dot x = \tilde Ax + \tilde Bu$, where x belongs to Hilbert space $R^n \times L_2 ([ - h,0],R^n )$ denoted as $M_2 $, and $\tilde A$ generates a $C_0 $-semigroup. It is shown that useful, practically verifiable conditions can be obtained by this approach.The following problems are investigated: approximate controllability in the space $M_2 $ and its subspace, $L_2 $, exact Euclidean $(R^n )$ controllability, spectral controllability, feedback stabilizability and a relation between pointwise degeneracy and function space controllability. Starting from the abstract functional analytic framework, the analysis is carried down to the matrix theory level, through the crucial intermediate role of the theory of entire functions.
Controllability, Control problems for functional-differential equations, function space controllability, approximate controllability, feedback, spectral controllability, linear retarded systems, Groups and semigroups of linear operators, Linear systems in control theory, Stabilization of systems by feedback, Control/observation systems in abstract spaces
Controllability, Control problems for functional-differential equations, function space controllability, approximate controllability, feedback, spectral controllability, linear retarded systems, Groups and semigroups of linear operators, Linear systems in control theory, Stabilization of systems by feedback, Control/observation systems in abstract spaces
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