Stabilization with J-dissipative controllers

Authors:	Kaneko Osamu, Osaka University, Japan Rapisarda Paolo, University of Maastricht, Netherlands
Topic:	2.2 Linear Control Systems
Session:	Control in a Behavioral Setting
Keywords:	stabilization, dissipativity, interconnection, quadratic differenial forms, metric interpolation problem

Abstract

Let $J=\diag(1,-1)$, and let $\mathfrak{B}$ be a controllable behavior. Let $\mathfrak{B}_{\mbox{\tiny des}}$ be a stable, autonomous subspace of $\mathfrak{B}$ representing the desired behavior after feedback interconnection with some controller$\mathfrak{C}$. In this paper we address the following questions:does there exist a $J$-dissipative controller $\mathfrak{C}$ suchthat $\mathfrak{C}\cap \mathfrak{B}=\mathfrak{B}_{\mbox{\tinydes}}$? How many unstable poles does the transfer functionassociated with the controllable part of $\mathfrak{C}$ have?