Sufficient and necessary conditions of exponential stabilisation for a class of distributed second-order semilinear systems with time delay

Abstract

In this paper, we investigate the problem of exponential stabilisation for a class of retarded distributed second-order semilinear systems by means of a bounded feedback control. The existence and uniqueness of mild solution for the considered systems are proved in Hilbert space framework. Sufficient and necessary conditions for exponential stabilisation are given. Some illustrating applications are provided.

Keywords:

• Semilinear systems
• second order
• feedback control
• exponential stabilisation
• decay estimate
• time delay

Disclosure statement

No potential conflict of interest was reported by the author(s).