A Unified Stability Analysis Approach for a Class of Interconnected System

From the structural perspective, this paper investigates a new formulation of the concept of input-to-state stability (ISS), and based on this formulation, proposes a new stability analysis approach for a class of interconnected system. The new formulation of ISS is better able to reflect the tendency of the state $x(t)$ tracking the input $u(t)$ and weakens the conservative of the original form. The stability analysis method which transforms the interconnected system into the equivalent cascade form, does not depend on the Lyapunov function, breaks through the limitation of the small-gain theorem and extends the application of ISS. As its applications in three typical kinds of interconnected systems, this method is used to prove the small-gain theorem again and analyzes the stability of a class of interconnected system and the consensus of the multi-agent system (MAS).