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Exponential Stability and Stabilization for Quadratic Discrete‐Time Systems with Time Delay
Author(s) -
Chen Fu,
Kang Shugui,
Qiao Shidong,
Guo Caixia
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.1540
Subject(s) - lemma (botany) , mathematics , quadratic equation , control theory (sociology) , discrete time and continuous time , stability (learning theory) , linear matrix inequality , exponential stability , lyapunov function , matrix (chemical analysis) , exponential function , mathematical optimization , computer science , nonlinear system , mathematical analysis , control (management) , ecology , statistics , physics , geometry , poaceae , materials science , quantum mechanics , artificial intelligence , machine learning , composite material , biology
In this note, we deal with the exponential stability and stabilization problems for quadratic discrete‐time systems with time delay. By using the quadratic Lyapunov function and a so called ‘Finsler's lemma', delay‐independent sufficient conditions for local stability and stabilization for quadratic discrete‐time systems with time delay are derived in terms of linear matrix inequalities (LMIs). Based on these sufficient conditions, iterative linear matrix inequality algorithms are proposed for maximizing the stability regions of the systems. Finally, two examples are given to illustrate the effectiveness of the methods presented in this paper.