L_{2}-stability of large-scale dynamical systems: Criteria via positive operator theory

A new approach to the L
2
-stability analysis of large-scale dynamical systems, described as interconnections of several subsystems, is presented. By conducting this study within the framework of positive operator theory, stability criteria, which impose explicit and distinct conditions on the subsystems and the interconnections, are obtained. Some strong points of the main result of the paper are: 1) it is simpler to apply than the existing results and 2) it specializes to the classical "positivity theorem" for the case of single-loop negative feedback systems. Modifications of this result which permit the use of arbitrary multipliers are also outlined.