A new notion of persistency-of-excitation for UGAS of NLTV systems: Application to stabilisation of nonholonomic systems

In this note we propose a new persistency of excitation condition for stability of nonlinear time-varying (NLTV) systems, which applies to adaptive systems with state-dependent regressor signals. We give sufficient conditions for uniform global asymptotic stability (UGAS). This result gives a transparent interpretation to the time-varying stabilization mechanism for nonholonomic systems. For 3-degrees-of-freedom chained systems we introduce the δ-PE stabilizers. These are smooth everywhere, and guarantee UGAS.