The $\mathcal{H}_{\infty,p}$ norm as the differential $\mathcal{L}_{2,p}$ gain of a $p$-dominant system

Padoan, A and Forni, F and Sepulchre, R The $\mathcal{H}_{\infty,p}$ norm as the differential $\mathcal{L}_{2,p}$ gain of a $p$-dominant system. In: UNSPECIFIED. (Unpublished)

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Abstract

The differential $\mathcal{L}_{2,p}$ gain of a linear, time-invariant, $p$-dominant system is shown to coincide with the $\mathcal{H}_{\infty,p}$ norm of its transfer function $G$, defined as the essential supremum of the absolute value of $G$ over a vertical strip in the complex plane such that $p$ poles of $G$ lie to right of the strip. The close analogy between the $\mathcal{H}_{\infty,p}$ norm and the classical $\mathcal{H}_{\infty}$ norm suggests that robust dominance of linear systems can be studied along the same lines as robust stability. This property can be exploited in the analysis and design of nonlinear uncertain systems that can be decomposed as the feedback interconnection of a linear, time-invariant system with bounded gain uncertainties or nonlinearities.

Item Type: Conference or Workshop Item (UNSPECIFIED) math.OC math.OC cs.SY eess.SY UNSPECIFIED Div F > Control Cron Job 07 Oct 2019 20:00 10 Dec 2019 02:04