On The Stability And ISS Of Nonlinear Singularly Perturbed Control Systems

In this paper, we present a set of interconnection conditions with the small-gain like property under which an input-to-state stability (ISS) property of nonlinear singularly perturbed systems with input is guaranteed by ISS of its slow and fast subsystems uniformly in the frozen slow variable. Moreover, we provide an explicit and closed form of stability bound on perturbation parameter and discuss some other cases. Meanwhile, a GAS property of nonlinear singularly perturbed systems is obtained as a particular case of ISS. Finally two examples are included to illustrate the applications of the results.This paper is organized mainly in three parts:The first part is an introduction. In this part, we first introduce the background of the studied problem and present some notions and results in the previous literatures.The second part is the main theorems and their detailed proof. Meanwhile, two examples are given to show the validity of the results.The third part is a summery of this paper.