• nonlinear descriptor system;
  • distributed delay;
  • exponential stability;
  • state feedback controller


This paper discusses the exponential stability and stabilization for nonlinear descriptor systems with discrete and distributed delays. In terms of the Lyapunov method, the exponential stability of the slow subsystem is firstly obtained. Then, a new homotopy-based approach is proposed to investigate the exponential stability of the fast subsystem. By an estimate of the weighted matrix norm for a nonlinear mapping, the exponential stability of the fast subsystem and thus delay-dependent sufficient conditions for the exponential stability of the systems are obtained. In addition, a state feedback controller is designed for the stabilization of the nonlinear descriptor systems. Finally, the effectiveness of the proposed approach is illustrated by numerical examples. Copyright © 2012 John Wiley & Sons, Ltd.