CONTROLLABILITY OF RETARDED DYNAMICAL-SYSTEMS

In the paper linear abstract retarded dynamical systems defined in inf inite-dimensional Hilbert spaces are considered. Using frequency-domai n methods and spectral analysis for linear selfadjoint operators neces sary and sufficient conditions for approximate relative controllabilit y are formulated and proved. The method presented in the paper allows to verify approximate relative controllability for abstract retarded d ynamical systems by consideration approximate controllability of suita ble simplified abstract dynamical systems without delays. Moreover, as an illustrative example approximate relative controllability of retar ded distributed parameter dynamical system is investigated. Presented results extend to more general class of retarded dynamical systems con trollability theorems known in the literature.