Bounds for Input- and State-to-Output Properties of Uncertain Linear Systems
For control engineers analyzing uncertain linear systems, this work offers a computationally tractable method to obtain informative bounds on system gains, though it is an incremental improvement over existing worst-case approaches.
This paper presents convex algorithms that produce parametric bounds on the L2-induced input-to-output and state-to-output gains for uncertain linear systems, providing quantitative information about how parametric uncertainty affects system performance.
We consider the effect of parametric uncertainty on properties of Linear Time Invariant systems. Traditional approaches to this problem determine the worst-case gains of the system over the uncertainty set. Whilst such approaches are computationally tractable, the upper bound obtained is not necessarily informative in terms of assessing the influence of the parameters on the system performance. We present theoretical results that lead to simple, convex algorithms producing parametric bounds on the $\mathcal{L}_2$-induced input-to-output and state-to-output gains as a function of the uncertain parameters. These bounds provide quantitative information about how the uncertainty affects the system.