A Generalized Matrosov Theorem for Signal Sets on Time Scales

The Matrosov theorem is used to infer uniform asymptotic stability of the trivial solution in the context of time-varying systems using a weak Lyapunov function. This paper generalizes the classic Matrosov theorem to dynamical systems, that exhibit continuous-time and discrete-time signals simultaneously. Such systems can be defined using the notion of time scales. We use the framework of Signal Sets equipped a pseudo distance measure to describe convergence, to obtain a generalized Matrosov theorem for dynamical systems defined on time scales. Two examples show how our results can be used to conclude uniform global attractivity of the trivial solution of a time-varying system, for which it appears that the existing Matrosov results fall short.