Robust Stability Of A Class Of Nonlinear Perturbations With Varying Delay Systems

Stability analysis for time-delay systems is the basis of the research for system theory. In recent years, a lot of outcomes with respect to the stability of time-varying delay systems have been found. In practice, nonlinear perturbations often appear in system modeling which may cause system instability, therefore, the study of the time-varying delay systems with nonlinear perturbations has important significance.This thesis mainly studies the stability of a class of time-varying delay systems with nonlinear perturbations. By using Lyapunov-Krasovskii functional, Jesen inequality, reciprocally convex approach, a new stability criterion is obtained in terms of linear matrix inequalities (LMI). Numerical examples are given to illustrate the effectiveness and advantage compared with the present results. The main contents are as follows:The problem of the stability of the time-varying delay systems with nonlinear perturbations is studied. By constructing a new Lyapunov functional, using Jesen inequality and reciprocally convex approach, a new stability criterion is established. Numerical examples are given to demonstrate the improvement of the results.The robust stability of a class of uncertain time-varying delay systems with nonlinear perturbations is investigated. A new robust stability criterion is given by using the method related to uncertainties, Schur complement lemma, delay decomposition method, and the matrix inequalities. Numerical examples demonstrate the effectiveness and advantage of the present results of this paper.