Well-posedness and Exponential Stability of Nonlinear Descriptor Systems with Discrete and Distributed Delays ?

This paper discusses the well-posedness and exponential stability for nonlinear descriptor systems with discrete and distributed delays. The existence and uniqueness of the solution to the systems is first demonstrated by using the Picard’s method. In terms of the Lyapunov method, the exponential stability of the slow subsystems is obtained. From the existence and uniqueness of the solution, a new homotopybased approach is proposed to investigate the exponential stability of the fast subsystems and thus some sufficient conditions for the exponential stability of the systems are obtained. Finally, the effectiveness of the proposed approach is illustrated by a numerical example.