Stability of impulsive differential systems with state-dependent impulses via the linear decomposition method

In this paper, we discuss the stability problem of the impulsive differential systems with state-dependent impulses. By using the linear decomposition methods, some sufficient conditions ensuring stability of the impulsive differential systems with state-dependent impulses are obtained and the estimate of the solution of such nonlinear systems is also acquired. Our results improve and generalize some of the known results given in earlier references. An example is given to demonstrate our results.