A Unified Stability Analysis Approach for a Class of Interconnected System
For control theorists, this work offers a less conservative ISS formulation and a novel Lyapunov-free stability analysis method that broadens the applicability of ISS to interconnected systems, though the results are theoretical and incremental in nature.
This paper proposes a new formulation of input-to-state stability (ISS) that better reflects state-input tracking and weakens conservatism, and introduces a Lyapunov-free stability analysis method that transforms interconnected systems into cascade form, extending ISS applications. The method is applied to reprove the small-gain theorem, analyze stability of a class of interconnected systems, and achieve consensus in multi-agent systems.
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).