Exponential stabilization of nonlinear uncertain systems with time-varying delay

The problem of robust exponential stabilization for dynamical nonlinear systems with uncertainties and time-varying delay is investigated. Based on the Razumikhin theorem and the Lyapunov function method, the continuous state feedback controllers for the studied systems are proposed and the robust exponential stabilization criterion is established in terms of solutions to the standard Riccati differential equations. Furthermore, a delay-dependent stabilization criterion is derived in terms of a linear matrix inequality and the restriction on the derivative of the delay function is removed. Finally, two numerical examples are presented to demonstrate the validity of the proposed method.