Please use this identifier to cite or link to this item: https://hdl.handle.net/2440/121980
Citations
Scopus Web of Science® Altmetric
?
?
Type: Journal article
Title: Necessary and sufficient conditions of exponential stability for delayed linear discrete-time systems
Author: Li, H.
Zhao, N.
Wang, X.
Zhang, X.
Shi, P.
Citation: IEEE Transactions on Automatic Control, 2019; 64(2):712-719
Publisher: IEEE
Issue Date: 2019
ISSN: 0018-9286
1558-2523
Statement of
Responsibility: 
Haifang Li, Ning Zhao, Xin Wang, Xian Zhang, and Peng Shi
Abstract: This paper is concerned with the problem of stability analysis for delayed linear discrete-time systems (DLDTSs). In order to obtain the necessary and sufficient criteria of exponential stability for DLDTSs, we first address the boundary value problem (BVP) of matrix difference equations, which is a generalization of the Lyapunov matrix equation (LME) for delay-free linear discrete-time systems. Also, the existence, uniqueness, and properties of solution to the BVP are investigated. In addition, for DLDTSs, we introduce a new concept-Lyapunov matrix that can be viewed as a generalization of the unique positive definite solution of delay-free LME. It should be noted that the Lyapunov matrix can be represented by the solution of the BVP. Then, the Lyapunov condition-a necessary and sufficient condition that guarantees the existence and uniqueness of Lyapunov matrix is introduced and characterized. Furthermore, by constructing Lyapunov matrix-based complete Lyapunov-Krasovskii functional, some necessary and sufficient conditions under which the considered DLDTSs are exponentially stable are proposed. Finally, two numerical examples are presented to show the advantages of the proven theoretic results.
Keywords: Boundary value problem; complete type Lyapunov–Krasovskii functional; delayed linear discrete-time systems; exponential stability; Lyapunov matrix; matrix difference equations
Rights: © 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.
DOI: 10.1109/TAC.2018.2830638
Appears in Collections:Aurora harvest 8
Electrical and Electronic Engineering publications

Files in This Item:
There are no files associated with this item.


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.