Passification‐based adaptive control of linear systems: Robustness issues

Abstract

AbstractPassivity is a widely used concept in control theory having led to many significant results. This paper concentrates on one characteristic of passivity, namely passification‐based adaptive control. This concept applies to multi‐input multi‐output systems for which exists a combination of outputs that renders the open‐loop system hyper‐minimum phase. Under such assumptions, the system may be passified by both high‐gain static output feedback and by a particular adaptive control algorithm. This last control law is modified here to guarantee its coefficients to be bounded. The contribution of this paper is to investigate its robustness with respect to parametric uncertainty. Time response characteristics are illustrated on examples including realistic situations with noisy output and saturated input. Theoretical results are formulated as linear matrix inequalities and can hence be readily solved with semi‐definite programming solvers. Copyright © 2007 John Wiley & Sons, Ltd.