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

TL;DR

This paper introduces a dissipativity framework for uncertain differential-algebraic systems, providing verifiable conditions for stability and performance bounds, demonstrated through power network analysis.

Contribution

It develops a novel dissipativity characterization for uncertain DAE systems using IQCs, with efficient verification methods for polynomial and linear cases.

Findings

Conditions for dissipativity can be verified via sum-of-squares or semidefinite programming.

Application to power networks shows minimal conservatism and computational tractability.

Framework unifies stability and performance analysis for uncertain DAE systems.

Abstract

This paper presents a novel framework for characterizing dissipativity of uncertain systems whose dynamics evolve according to differential-algebraic equations. Sufficient conditions for dissipativity (specializing to, e.g., stability or $L_2$ gain bounds) are provided in the case that 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. Performance analysis of the IEEE 39-bus power network with a set of potential line failures modeled as an uncertainty set provides an illustrative example that highlights the computational tractability of this approach; conservatism introduced in this example is shown to be quite minimal.