Backstepping Design for Robust Stabilizing Control of Nonlinear Systems with Time-Delay

Authors:	Shen Tielong, Sophia University, Japan Jiao Xiaohong, Tsinghua University, China Sun Yuanzhang, Tsinghua University, China
Topic:	2.5 Robust Control
Session:	Robust Controller Synthesis I
Keywords:	Time delay, nonlinear system, Lyapunov-Razumikhim function, stabilization

Abstract

Backstepping design forrobust stabilizing control of nonlinear systems with time-delay isinvestigated in this paper. It is shown that the backsteppingdesign for time-delay systems based on the Lyapunov-Razumikhinfunction is not a trivial extension of the case of nonlinearnondelay systems due to the existence of the Razumikhin condition.The key point is how to deal with the non-triangular structureform of the system after application of the Razumikhin condition.A design technique to overcome the obstacle is given so that adelay-independent state feedback stabilizing control law can beexplicitly obtained by step-by-step recursion based on theconstruction of the Lyapunov-Razumikhin function.