Rapidly Time-Varying Systems

Abstract

In the first nine chapters, we considered continuous time and discrete time systems with a single time scale. We turn next to continuous time systems with two continuous time scales, one faster than the other. Systems of this kind are called either rapidly time-varying systems or slowly time-varying systems. The presence of multiple time scales significantly complicates the problem of constructing global strict Lyapunov functions. In this chapter, we provide a systematic method for rapidly time-varying systems. Our main method involves transforming Lyapunov functions for the corresponding limiting dynamics into the desired strict Lyapunov functions for the original rapidly time-varying dynamics. We illustrate our findings using a one degree-of-freedom mass-spring system.