The H_{∞,p} norm as the differential L_{2,p} gain of a p-dominant system
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Padoan, Alberto https://orcid.org/0000-0003-1597-0395
Forni, Fulvio https://orcid.org/0000-0002-5728-0176
Sepulchre, Rodolphe https://orcid.org/0000-0002-7047-3124
Abstract
The differential L2,p gain of a linear, time- invariant, p-dominant system is shown to coincide with the H∞,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 H∞,p norm and the classical H∞ 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.
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58th Conference on Decision and Control
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Royal Society (RGS\R1\191308)