Certifying Stability and Performance of Uncertain Differential-Algebraic Systems: A Dissipativity Framework

Abstract

This paper presents a novel framework for characterizing dissipativity of uncertain dynamical systems subject to algebraic constraints. The main results provide sufficient conditions for dissipativity when uncertainties are characterized by integral quadratic constraints. For polynomial or linear dynamics, these conditions can be efficiently verified through sum-of-squares or semidefinite programming. The practical impact of this work is illustrated through a case study that examines performance of the IEEE 39-bus power network with uncertainties used to model a set of potential line failures