Robustness Analysis of Uncertain Discrete-Time Systems with Dissipation Inequalities and Integral Quadratic Constraints

This 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 c © 0000 John Wiley & Sons, Ltd.