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Indexed by:期刊论文

Date of Publication:2011-10-01

Journal:SYSTEMS & CONTROL LETTERS

Included Journals:Scopus、SCIE、EI

Volume:60

Issue:10

Page Number:832-839

ISSN No.:0167-6911

Key Words:Stability; Quadratic constraint; Completely finite; Nest algebra; Connected uncertainty set; Gap metric; Time-varying system

Abstract:In this paper, we introduce the concept of "quadratic constraint" (QC) to deal with various stability problems for infinite dimensional linear discrete time-varying (LW) systems. First, we derive a necessary and sufficient condition for the close-loop stability based on quadratic constraints (QCs). An equivalent condition of this stability criterion presents the relationship between the stabilization of each finite dimensional truncation system and that of the whole system. Moreover, applying this stability criterion and the complete finiteness of the nest algebra, we show that the plant is stabilizable if and only if it has a single strong representation. Finally, we use QCs to give a necessary and sufficient condition for the robust stabilization of connected uncertainty set defined by gap metric. (C) 2011 Elsevier B.V. All rights reserved.