On the stability of nonlinear systems with respect to a part of the variables and application

This paper is concerned with the study of the problem of stability with respect to a part of the variables of nonautonomous systems. A new class of perturbed nonlinear systems is derived to guarantee the global exponential convergence of the solutions toward a small ball centered at the origin. We state some sufficient conditions based on generalized integral inequalities of Gronwall type. Furthermore, as an application we consider the stabilization problem of time-varying perturbed control system.