Lyapunov Functions for Linear Time-varying Systems

Abstract

A systematic method of generating explicit Lyapunov functions for linear time-varying differential equations is presented in this paper. The linear time-varying system equation is decomposed into a fixed part and a time-varying part. A simple closed form expression of the Lyapunov function for the fixed part has been derived. This has been suitably augmented and applied to the time-varying system in the determination of stability results. Only first-order time-derivatives on the time-varying parameters of the system are involved in the stability results.