An Extended Small-Gain Theorem

TL;DR

This paper extends the small-gain theorem to use general vector norms for interconnected systems, providing more flexible control design by explicitly characterizing subsystem gains.

Contribution

It introduces a generalized small-gain theorem that incorporates vector norms and subsystem gains, enhancing control system analysis and design.

Findings

Allows use of general vector norms for input-output characterization

Provides explicit subsystem gain information

Enhances flexibility in control system design

Abstract

We extend the results of the general small-gain theorem proposed by Z.P Jiang. The significance of this extension is two fold. First, it allows one to use general vector norm to characterize the input-to-output property of two interconnected subsystems. Second, the gain from input signals to output of each sub-system is provided, which offers one more flexibility in control design.