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

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