Well-posedness and asymptotic stability of nonlinear equations with delay and application in descriptor systems

There have been many criteria on well-posedness and asymptotic stability for nonlinear algebra equations with delay. However, it is inconvenient to discuss descriptor systems by using these criteria. In this paper, new sufficient conditions for well-posedness and asymptotic stability of nonlinear algebra equations with delay are given. Based on these conditions, the criteria on well-posedness and asymptotic stability for nonlinear descriptor systems with delay are proposed conveniently. Finally, the effectiveness of the approach is illustrated by a numerical example.