An output stabilization of bilinear distributed systems

Abstract

The aim of this paper is to study regional stabilization of the flux of bilinear distributed systems. More precisely it consists in studying the asymptotic behavior of the gradient of such a system not in its whole geometrical evolution domain Ω but only in a subregion ω of Ω. Then we give definitions and under suitable condition we give gradient stabilizing control. We also characterize the control which stabilizes regionally the gradient, and minimizes a given performance cost. Then we develop a numerical approach that is successfully illustrated by simulations.

On the output feedback stabilization for distributed semilinear systems

“…, (12) where M = (2 TL 2 + 1)T 1 2 is a non-negative constant depending on ||z 0 || and T. From hypothesis 1 of Theorem 1, we have…”