Exact controllability and complete stabilizability for linear systems in Hilbert spaces
Linear, stationary, infinite-dimensional continuous-time control systems defined in Hilbert spaces are considered. Using methods of functional analysis, necessary and sufficient conditions for exact controllability in finite time are formulated and proved. Next, the relationships between exact controllability and complete stabilizability are discussed. It is shown, that with minimal assumptions concerning the semigroup generated by system operator, complete stabilizability implies exact controllability. Moreover, many remarks and comments on exact controllability and complete stabilizability are given. Similar exact controllability problems have been considered in the paper [\textit{J. C. Louis} and \textit{D. Wexler}, J. Differ. Equ. 49, 258-269 (1983; Zbl 0505.49018)].
scientific article; zbMATH DE number 1078532
scientific article