2019/09/26 by Alberto Padoan, Padoan, Alberto, Fulvio Forni +3
Computer Science · Engineering · Mathematics · #Control and Stability of Dynamical Systems #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #Stability and Controllability of Differential Equations #Systems and Control (eess.SY) #cs.SY #eess.SY #electronic engineering #information engineering #math.OC
paper · pdf · doi:10.48550/arxiv.1909.12202
6 pages, 3 figures, 58th IEEE Conf. Decision and Control
arxiv created 2019/09/26 · openalex publication_date 2019/09/26 · arxiv updated 2019/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.