Linear time-varying systems in Hilbert spaces: Exact controllability implies complete stabilizability

P. Niamsup, V. N. Phat

Abstract

This paper deals with the problem of controllability and stabilizability of linear time-varying control systems in Hilbert spaces. We prove that any globally null-controllable system is completely stabilizable and conversely, under some additional conditions the complete stabilizability implies the global null-controllability. The obtained result extends existing results in the literature to infinite-dimensional and time-varying control systems.