Novel Stability Criteria of Nonlinear Systems with Uncertainties and Time-varying Delay

The problem of robust stabilization for a class of dynamical nonlinear systems with uncertainties and time-varying delay is discussed. On condition that the derivative of time-varying delay function has restriction, a novel stability criterion which can guarantee the exponential stabilization of the system is established by using the Riccati differential equation. Furthermore, when there is no bound restriction on the derivative of time-varying delay function, a continuous state feedback controller is proposed and a sufficient condition for the stability of the system is derived by combining the Riccati differential equation with the Razumikhin Stability Theorem. It is worth while to note that, in our proposed design method, the nonlinear perturbation and the derivative of the time-varying delay function both have no bound restriction. Finally, a numerical example is given to demonstrate the validity of the result.