/spl delta/-persistency of excitation: a necessary and sufficient condition for uniform attractivity

In previous papers we have introduced a sufficient condition for uniform attractivity of the origin of a class of nonlinear time-varying systems which is stated in terms of persistency of excitation (PE), a concept well known in the adaptive control and systems identification literature. The novelty of our condition, called uniform /spl delta/-PE, is that it is tailored for nonlinear functions of time and state and it allows us to prove uniform asymptotic stability. In this paper we present a new definition of u/spl delta/-PE which is conceptually equivalent to but technically different from its predecessors. We make connections between this property and similar properties previously used in the literature. We also show when this condition is necessary and sufficient for uniform (global) asymptotic stability for a large class of nonlinear time-varying systems.