Exponential stabilisation of delayed distributed semilinear systems in Banach spaces

Abstract

In this paper, we deal with the problem of stabilisation for a class of distributed semilinear systems. The considered systems present a state time delay and evolve in Banach spaces. A new stabilising feedback control is proposed. Two kinds of stabilizability, namely exponential and weak stabilizability, are investigated. An explicit estimate of the energy decay rate is given. Some illustrating applications to parabolic and hyperbolic equations with numerical simulations are considered.

Keywords:

• Semilinear systems
• Banach spaces
• duality mapping
• weak stabilisation
• exponential stabilisation
• time delay

Disclosure statement

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