Generalized dilations and the stabilization of uncertain systems via measurement feedback

We study the problem of semiglobally stabilizing uncertain nonlinear system z = Az + Bu + p(1)(z,u,t)u, y =z + p(2)(z,u,t)u, with (A, B) in Brunowski form. We prove that if p(1)(z, u, t)u and p(2)(z, u, t)u are of order great er than 1 and 0, respectively, with "generalized" dilation delta (1)(z, u)= (l(1-n) z(1),.... l(-1)z(n-1),z(n), lu) and uniformly with respect to r, wh ere z(i) is the ith component of z, then we can achieve semiglobal stabiliz ation via arbitrarily bounded linear measurement feedback. (C) 2001 Elsevie r Science B.V. All rights reserved.