Input-to-state stability of the nonlinear singular systems via small-gain theorem

Abstract This paper presents the input-to-state stability (ISS) of nonlinear singular systems (NSSs) based on the small-gain theorem of singular system. The major contribution of this paper includes three aspects. Firstly, give and prove the existence and unique conditions for the solution of NSS based on the fast-slow subsystem. Secondly, the conditions of ISS property for the NSSs are obtained via the small-gain theorem, and a method for constructing ISS-Lyapunov function of NSSs is presented. Thirdly, the theorems for input-to-state practical stability (ISpS) and the trajectory-based small-gain theorem of interconnected NSSs are proposed. Finally, the effectiveness of proposed method is illustrated by using a circuit network model and a numerical example.