Performance robustness of a class of systems with multilinearly correlated perturbations
type: Item
instance of: scholarly article
title: Performance robustness of a class of systems with multilinearly correlated perturbations
zbMATH Open document ID: 0856.93081
author: Lin Huang
author: Long Wang
published in: Science in China. Series A
publication date: 1997-02-25T00:00:00Z
review text: The robustness study of interval systems or linearly perturbed systems is nearing maturity, whereas the robustness study of multilinearly or nonlinearly perturbed systems is still in its infancy. For a family of shifted and rotated systems with multilinearly correlated perturbations the strict positive realness of the entire family can be inferred from the same property of its vertex systems. The main results of the paper show that the maximal \(H^\infty\) norm of a family of shifted systems with multilinearly correlated perturbations is obtained at its vertex systems. Thus, the robustness issues of strict positive realness and \(H^\infty\) norm are unified in one theoretical framework. Two well-known strong sixteen-vertex-verification Kharitonov-like theorems on performance robustness of an interval system family are direct consequences of the above results. The results presented in the paper are also suitable for the robust absolute stability analysis of uncertain systems. The paper is mathematically dense. The references are somewhat antiquated.
reviewed by: A.S.Hauksdottir
Mathematics Subject Classification ID: 93D09
Mathematics Subject Classification ID: 93D10
Mathematics Subject Classification ID: 93B36
Mathematics Subject Classification ID: 93B35
Mathematics Subject Classification ID: 93C73
zbMATH DE Number: 850851
zbMATH Keywords: uncertain systems
zbMATH Keywords: finite verification
zbMATH Keywords: vertex
zbMATH Keywords: robustness
zbMATH Keywords: interval systems
zbMATH Keywords: multilinearly correlated perturbations
zbMATH Keywords: strict positive realness
zbMATH Keywords: \(H^ \infty\) norm
zbMATH Keywords: Kharitonov-like theorems
zbMATH Keywords: performance robustness
zbMATH Keywords: robust absolute stability
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 850851