Quadratic stabilization of uncertain control systems with time varying delays

The stabilization of a class of uncertain control systems with time-varying delays was studied. Such an uncertain control system with time-varying delays was described by time-varying unknown-but-bounded uncertain parameters. By using the linear matrix inequalities and the quadratic Lyapunov-Krasovskii functional, some stability criterions were derived to ensure that the system was stable. Based on these criterions, the problem was solved via state feedback controller, guaranteeing the resultant closed-loop system was robustly stable. Finally, a numerical example was given to illustrate the validity of the results.