On exponential stability of infinite dimensional linear systems with bounded or unbounded perturbations

Abstract

In this paper, we study the question of stabilization of uncertain systems governed by evolution equations in Ililbert space. It is shown that exponential stability can be achieved by choice of suitable state feedback controls even in the presence of bounded or relatively bounded (uncertain) perturbations. Our proof is based on perturbation theory of semigroups. The results are illustrated by two examples involving heat equation and wave equation.

Keywords:

• Infinite dimensional Systems
• Stabilizability
• Exponential stability
• Relative bounded perturbations
• m-dissipativity
• feedback control

AMS(MOS)::

• 93C25
• 93D15
• 93D20