On the Stability and Controllability of Degenerate Differential Systems in Hilbert Spaces

Abstract

We apply the famous theorem of Lyapunov for some degenerate differential systems taken the form Ax’(t) + Bx(t) = Φ(t, x(t)), where t∈R+ and A, B are linear bounded operators in Hilbert spaces, Φ is a given function. The obtained results are used to study the stabilizability and controllability of certain implicit controlled systems.