UGAS of Skew-symmetric Time-varying Systems: Application to Stabilization of Chained Form Systems

Abstract

The contribution of this communication is twofold: firstly, we will present a theorem guaranteeing uniform global asymptotic stability of a class of stable nonlinear systems, known in the literature of nonholonomic systems as skew-symmetric. These are systems of the form x ˙ = − A ( t , x ) x where A ( . , . ) e R n × n is skew-symmetric except for the (1,1) element which is non-zero. Secondly, we extend previous results for the nonholonomic integrators to the case of systems with n>3 states. Our smooth time-varying controllers are called δ-persistently exciting since they are based on a property which generalizes for nonlinear functions of the state, the persistency of excitation concept originally defined for time functions, in the context of systems identification.