Strong stabilisation and decay estimate for unbounded bilinear systems

Abstract

In this article, we deal with distributed bilinear systems, where the operator of control is supposed to be unbounded in the sense that it is bounded from the state space into some extension. Then we give sufficient conditions for strong stabilisation. Also the rate of convergence of the state is estimated. An illustrating example is given.

Keywords:

• unbounded bilinear system
• feedback stabilisation
• decay estimate