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Stability analysis and H ∞ control design for a class of nonlinear time‐delay systems
Author(s) -
Yang Renming,
Wang Yuzhen
Publication year - 2012
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.276
Subject(s) - control theory (sociology) , nonlinear system , stability (learning theory) , jacobian matrix and determinant , mathematics , invertible matrix , weighting , matrix (chemical analysis) , class (philosophy) , computer science , control (management) , medicine , physics , materials science , quantum mechanics , artificial intelligence , machine learning , pure mathematics , composite material , radiology
This paper investigates the stability and H ∞ control problem for a class of nonlinear time‐delay systems with a nonsingular Jacobian matrix, and provides a number of new results regarding stability analysis and control design. Firstly, an equivalent form is obtained for this class of systems by means of coordinate transformation and/or orthogonal decomposition of vector fields. Then, based on the equivalent form and free‐weighting matrix method, several sufficient conditions, in terms of nonlinear matrix inequalities, are derived for the stability analysis of the time‐delay systems by constructing suitable Lyapunov functionals. Finally, we use the equivalent form and the obtained stability results to investigate the H ∞ control problem, and present a control design procedure for this class of time‐delay systems. A study of illustrative examples shows that the results obtained in this paper have less conservatism, and work very well in the stability analysis and control design of some nonlinear time‐delay systems.Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society