Exponential stabilization for nonlinear systems with delayed perturbations

The problem of stabilization for dynamical systems with delayed perturbations is considered. Firstly, a class of nonlinear systems with delayed perturbations is studied. Some sufficient conditions are derived by making use of Lyapunov stability theory, and a continuous controller is provided for the exponential convergence of the systems with delayed perturbations. Then, a class of nonlinear systems with delayed perturbations and uncertain control is concerned. A continuous feedback controller is constructed, and the corresponding closed-loop system satisfying some conditions can be proved to be exponentially stable. Furthermore, a class of uncertain systems with linear nominal part is investigated. It is proved that the class of systems is exponential stabilizable under certain appropriate conditions. Finally, a numerical example is given to demonstrate the validity of the results.