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WDOP‐based Summation Inequality and its Application to Exponential Stability of Linear Delay Difference Systems
Author(s) -
Zhang Xian,
Shang Wanzhen,
Wang Yantao
Publication year - 2018
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1597
Subject(s) - orthogonalization , mathematics , exponential stability , exponential function , stability (learning theory) , set (abstract data type) , mathematical analysis , algorithm , nonlinear system , computer science , physics , quantum mechanics , machine learning , programming language
This paper is concerned with the exponential stability analysis of linear delay difference systems. Firstly, a set of weighted discrete orthogonal polynomials (WDOPs) is established by using the Gram‐Schmidt orthogonalization process, and then two WDOPs‐based summation inequalities, including some existing summation inequalities as special cases, are developed. Secondly, these WDOPs‐based summation inequalities are applied to investigate the exponential stability criteria and explicit exponential estimates of solutions of linear delay difference systems. Finally, two numerical examples indicate that the proposed WDOPs‐based approach can derive the exponential stability condition with larger decay rate than the existing ones.