Stability analysis and H∞ control design for a class of nonlinear time-delay systems

Abstract

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