A Generalization of Morse's Theorem for Nonlinear Time-Varying Systems
Abstract
The paper investigates uniform asymptotic stability (UAS) for nonlinear time-varying (NTV) systems from the state-output viewpoint. Uniform Lyapunov stability (ULS) of the origin is first guaranteed by employing a new detectability condition and an integral inequality relating to output function. In addition to a newly developed criterion for attractivity, a novel result for UAS can then be proposed without assuming the ULS property in priori. It extends a theorem proposed by Morse to NTV systems. Moreover, the observability conditions often assumed in present literature can be relaxed by using detectability based on our approaches.
