Exponential stability and asymptotic stability for nonlinear singular impulsive systems

This paper discusses exponential stability and asymptotic stability for nonlinear singular impulsive systems with the first jumping discontinuity points. A necessary and sufficient condition for the existence and uniqueness of piecewise continuous solution to the systems is firstly presented. Based on this, we give different jumping condition with other articles. Then, a criterion on the exponential stability for the systems is given in terms of linear matrix inequalities(LMIs). Some improved results are follows on exponential stability and asymptotic stability. Finally, the effectiveness of the approach is illustrated by a numerical example.