Limiting Zeroing-Output Solutions and Weak Detectability in Hybrid Nonlinear Time-Varying Systems

Checking the uniform attractivity of solutions of a time-varying dynamic system is challenging. Uniform attractivity concerns the limiting behaviors of trajectories, which in the context of hybrid nonlinear time-varying (NLTV) systems, is non-trivial due to the complexity of the system trajectories and the limits that are involved. This paper analyzes a specific class of limiting behaviors of hybrid NLTV systems ranging from limiting zeroing-output hybrid (ZOH) solutions to limiting ZOH systems. For these limiting behaviors, it is possible to define a novel notion of weak detectability (WD). It is shown that a particular solution set of a hybrid NLTV system is uniformly, globally, asymptotically stable provided it has the WD property, assuming that uniform global stability (UGS) and a bounded energy condition relative to two output maps hold as well. A simple example is used to illustrate the effectiveness of this result.