UGAS of nonlinear time-varying systems: A δ-persistency of excitation approach

We study the problem of stability analysis for certain nonlinear systems. Our contributions are new tools to guarantee uniform global asymptotic stability (UGAS) of nonlinear time-varying (NLTV) systems. First, we provide new definitions of persistency of excitation (PE). In particular, we give a new definition of uniform δ-PE (uG-PE) which, though conceptually equivalent to the original one we introduced (1999), is mathematically less conservative. We also provide with some properties of δ-PE pairs and contribute with a result which establishes UGAS of NLTV systems under uδ-PE