Robustness analysis of uncertain discrete‐time systems with dissipation inequalities and integral quadratic constraints

Abstract

SummaryThis paper presents a connection between dissipation inequalities and integral quadratic constraints (IQCs) for robustness analysis of uncertain discrete‐time systems. Traditional IQC results derived from homotopy methods emphasize an operator‐theoretic input–output viewpoint. In contrast, the dissipativity‐based IQC approach explicitly incorporates the internal states of the uncertain system, thus providing a more direct procedure to analyze uniform stability with non‐zero initial states. The standard dissipation inequality requires a non‐negative definite storage function and ‘hard’ IQCs. The term ‘hard’ means that the IQCs must hold over all finite time horizons. This paper presents a modified dissipation inequality that requires neither non‐negative definite storage functions nor hard IQCs. This approach leads to linear matrix inequality conditions that can provide less conservative results in terms of robustness analysis. The proof relies on a key J‐spectral factorization lemma for IQC multipliers. A simple numerical example is provided to demonstrate the utility of the modified dissipation inequality. Copyright © 2016 John Wiley & Sons, Ltd.