On Positive-Realness and Lyapunov Functions for Switched Linear Differential Systems.

We show new results about Lyapunov stability of switched linear differential systems (SLDS) using the concept of positive realness. The main results include stability conditions for a class of SLDS with augmented banks and the parametrization of families of asymptotically stable SLDS with three modes. Such conditions can be verified using LMIs that can be directly set up from the higher-order differential equations describing the modes.