Abstract
The composite-system method for analyzing stability of large-scale system is studied focusing on the quadratic-order theorems using <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> -matrices. Here, by the term "composite-system method", we refer to the method to decompose a large-scale system into smaller subsystems and to make two-step analysis (i.e., first to analyze subsystems and second to combine the results to reduce the property of the whole). Theories about Lyapunov stability and about input-output stability are described from a unified standpoint and their mutual relation is clarified. As an application, multi-input multi-output systems. The contents are generally useful for stability analysis of large-scale nonlinear systems.
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