On the Exponential Stability of the Implicit Differential Systems in Hilbert Spaces

Abstract

The aim of this research is to study the exponential stability of the stationary implicit system: Ax’(t) + Bx(t) = 0, where A and B are bounded operators in Hilbert spaces. The achieved results are the generalization of Liapounov Theorem for the spectrum of the operator pencil λA + B. We also establish the exponential stability conditions for the corresponding perturbed and quasi-linear implicit systems.