Stability Analysis and Estimate of Domain of Attraction for a Class of Nonlinear Systems with Time-varying Delay

This paper investigates the stability and estimate of domain of attraction for a class of nonlinear time-varying delay systems, and proposes a number of new results on both the stability and estimate of domain of attraction. Firstly, an equivalent form is obtained for the systems by means of coordinate transformation and orthogonal decomposition of vector fields. Then, based on the equivalent form and the free-weighting matrix method, several sufficient conditions in terms of nonlinear matrix inequalities are derived for the stability analysis by constructing suitable Lyapunov functionals. Finally, the equivalent form and the obtained stability results are applied to the estimate of domain of attraction for this class of nonlinear time-delay systems, and a new approach is presented. Illustrative examples show that the results obtained in this paper are effective in studying the stability and estimation of domain of attraction for the class of nonlinear time-delay systems.