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Robust Finite‐Time Stability and Stabilization of Linear Uncertain Time‐Delay Systems
Author(s) -
Stojanovic Sreten B.,
Debeljkovic Dragutin Lj.,
Antic Dragan S.
Publication year - 2013
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.689
Subject(s) - control theory (sociology) , linearization , mathematics , linear system , linear matrix inequality , stability (learning theory) , full state feedback , controller (irrigation) , time complexity , mathematical optimization , computer science , nonlinear system , control (management) , algorithm , mathematical analysis , physics , quantum mechanics , artificial intelligence , machine learning , agronomy , biology
Robust finite‐time stability and stabilization problems for a class of linear uncertain time‐delay systems are studied. The concept of finite‐time stability is extended to linear uncertain time‐delay systems. Based on the Lyapunov method and properties of matrix inequalities, a sufficient condition that ensures finite‐time stability of linear uncertain time‐delay systems is given. By virtue of the results on finite‐time stability, a memoryless state feedback controller that guarantees that the closed‐loop system is finite time stable, is proposed. The controller design problem is solved by using the linear matrix inequalities and the cone complementarity linearization iterative algorithm. Numerical examples verify the efficiency of the proposed methods.