Asymptotic stabilization of coupled oscillators with dry friction by feedback control

In this paper we design a feedback control u = u(x, (x) over dot) so that each solution x(.) of the closed-loop system (x) double over dot (t) + partial derivative Phi((x) over dot) + Delta del f (x) + u(x, (x) over dot) (sic) 0 approaches the set of critical points of f(x) with vertical bar(x) over dot(t)vertical bar -> 0 as t -> +infinity. The robustness of the control is also discussed in the case where (x) has only a finite number of critical values. The approach is mainly based on LaSalle's invariance principles and Morse decomposition theory of attractors for differential inclusions. (C) 2012 Elsevier Ltd. All rights reserved.