A Dynamic S-Procedure for Dynamic Uncertainties

TL;DR

This paper introduces a novel dynamic S-procedure for analyzing the robust stability of uncertain systems with dynamic uncertainties, using linear matrix inequalities and integral quadratic constraints.

Contribution

It presents a new method to compose stability tests for uncertain systems via a dynamic S-procedure based on dissipativity and integral quadratic constraints.

Findings

Formulated stability tests as LMIs for uncertain systems.

Connected frequency domain S-procedure with time-domain dissipativity.

Enabled potential extensions to time-varying and hybrid systems.

Abstract

We show how to compose robust stability tests for uncertain systems modeled as linear fractional representations and affected by various types of dynamic uncertainties. Our results are formulated in terms of linear matrix inequalities and rest on the recently established notion of finite-horizon integral quadratic constraints with a terminal cost. The construction of such constraints is motivated by an unconventional application of the S-procedure in the frequency domain with dynamic Lagrange multipliers. Our technical contribution reveals how this construction can be performed by dissipativity arguments in the time-domain and in a lossless fashion. This opens the way for generalizations to time-varying or hybrid systems.