A theorem for UGAS and ULES of (passive) nonautonomous systems: robust control of mechanical systems and ships

The main contribution of this paper is a theorem to guarantee uniform globa l asymptotic stability (UCAS) and uniform local exponential stability (ULES ) for a class of nonlinear non-autonomous systems which includes passive sy stems. These properties (and a uniform local Lipschitz condition) guarantee robustness of stability while weaker properties, like uniform global stabi lity plus global convergence, do not. Our main result is then used in the t racking control problem of mechanical systems and ships. We use an adaptive backstepping design and prove UGAS of the closed-loop tracking error syste m, in particular, we obtain that both the tracking and parameter estimation errors converge uniformly globally to zero. Copyright (C) 2001 John Wiley & Sons, Ltd.