PROJECT TITLE :

Stability and Persistent Excitation in Signal Sets

ABSTRACT:

Persistent excitation (PE) conditions have been widely used to analyze stability properties of various parameter identification algorithms and to establish uniform international asymptotic stability (UGAS) for a large category of nonlinear time-varying systems. In order to generalize such conditions to a additional general setting, a brand new PE condition is proposed with three basic ingredients: a proof set to represent a family of your time functions (e.g., trajectories); a pseudo distance measure to describe the convergence; and a few binary relations (e.g., state-to-output relations). Closely related to detectability, this PE condition may be a necessary condition to guarantee UGAS. Under uniform international stability and an integral inequality, it becomes a sufficient condition of UGAS. A novel concept: M-combine, that aims at simplifying the checking of the PE condition, is introduced. By using M-pair, it's possible to simplify the structure of the referred signal set (in the spirit of the classic Krasovskii-LaSalle theorem) and to increase the dimension of the reference signal set (kind of like the Matrosov theorem). Therefore, the framework of M-combine not only unifies these well-known results, however also generates additional flexibility in checking the PE conditions. When applied to nonlinear switched systems, three new tools to verify the PE condition are obtained. Finally, an example illustrates that a nonlinear time-varying switched system with arbitrary switching will be shown to be UGAS while not employing a common Lyapunov perform.