PASSIVITY METHODS IN THE INPUT-OUTPUT STABILITY AND INSTABILITY OF LARGE-SCALE SYSTEMS.

Abstract A new approach to the L2-stability and L2-instability analysis of large-scale dynamical systems, described as an interconnection of several subsystems, is presented. Criteria which involve explicit and distinct passivity conditions on the subsystems and certain algebraic constraints on the interconnections are given. These are simpler and more general than the existing results for the stability and instability of large-scale systems and further have the following additional features: (i) they permit directly the use of arbitrary multipliers and (ii) they generalize some of the classical results for the stability and instability of single-loop negative feedback systems.