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 ofpositive 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 mode

Modeling and analysis of energy distribution networks using switched differential systems

It is a pleasure to dedicate this contribution to Prof. Arjan van der Schaft on the occasion of his 60th birthday. We study the dynamics of energy distribution networks consisting of switching power converters and multiple (dis-)connectable modules. We use parsimonious models that deal effectively with the variant complexity of the network and the inherent switching phenomena induced by power converters. We also present the solution to instability problems caused by devices with negative impedance characteristics such as constant power loads. Elements of the behavioral system theory such as linear differential behaviors and quadratic differential forms are crucial in our analysis