Global stabilization of a class of time-delay nonlinear systems

This paper is concerned with the problem of global stabilization by state feedback and output feedback for a class of time-delay nonlinear systems that are dominated by a triangular system satisfying linear growth conditions. By solving the Lyapunov equation and constructing the appropriate Lyapunov - Krasovskii functionals (LKF), the linear and memoryless state feedback controller and output feedback controller making the closed-loop system globally asymptotically stable ( GAS) are explicitly constructed respectively. Comparing our design scheme with the backstepping method which has been widely used to deal with strictly feedback nonlinear systems, our design scheme is much simpler and more efficient. An example is given to show that the proposed design procedures are very simple and efficient.