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

26 Sep 2019 Padoan Alberto Forni Fulvio Sepulchre Rodolphe

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... (read more)

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  • OPTIMIZATION AND CONTROL
  • SYSTEMS AND CONTROL
  • SYSTEMS AND CONTROL