  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).
