Complexity issues in robust stability of linear delay-differential systems
type: Item
instance of: scholarly article
title: Complexity issues in robust stability of linear delay-differential systems
zbMATH Open document ID: 0878.93050
DOI: 10.1007/BF01211858
author: Onur Toker
author: H. Özbay
published in: MCSS. Mathematics of Control, Signals, and Systems
publication date: 1998-01-05T00:00:00Z
review text: This paper discusses the linear differential systems with delays: \(\dot x(t)= A_0 x(t) +\sum^p_{k=1} A_k x(t-h_k)\), where \(A_0, \dots, A_p\) are \(n\times n\) constant matrices. Two stability problems concerning the systems, which are: i) asymptotic stability independent of delay; ii) robust asymptotic stability, are shown to be NP-hard. The main idea used in the proofs of the results is to show that the robust stability problems i) and ii) can be formulated as a combinatorial problem \((T\)-knapsack problem), which is known to be NP-hard. Also, another side result of the paper is that checking robust nonsingularity, robust Hurwitz stability, robust Schur stability of a disk matrix are NP-hard problems.
Mathematics Subject Classification ID: 93D09
Mathematics Subject Classification ID: 34K35
Mathematics Subject Classification ID: 68Q25
zbMATH DE Number: 1018718
zbMATH Keywords: linear delay-differential systems
zbMATH Keywords: computational complexity
zbMATH Keywords: complex programming
zbMATH Keywords: robust stability
zbMATH Keywords: NP-hard
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01211858
OpenAlex ID: W1998155875
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description: scientific article; zbMATH DE number 1018718