This paper is concerned with the stability of nonlinear time-varying perturbed system on time scales under the assumption that the corresponding linear time-varying nominal system is uniformly exponentially stable. Some less conservative sufficient conditions for uniform exponential stability and uniform practical exponential stability are proposed by imposing different assumptions on the perturbation term. Compared with the traditional exponential stability results of perturbed systems, the time derivatives of related Lyapunov functions in this paper are not required to be negative definite for all time. The main tools employed are two Gronwall's inequalities on time scales. Some examples are also given to illustrate the effectiveness of the theoretical results.

In this paper, the clustering component synchronization of nonlinearly coupled complex dynamical networks with nonidentical nodes was investigated. By applying feedback injections to those nodes who have connections with other clusters, some criteria for achieving clustering component synchronization were obtained. A numerical simulation was also included to verify the correctness of the results obtained.