Input-Output Stability and Response Analysis for Hierarchical Large-Scale Systems

Abstract Analysis of hierarchially structured, possibly nonlinear, large scale systems is found to be greatly simplified using a result that permits testing for stability and generation of conic sector bounds for the I/O relation of an interconnected system from conic sector bounds on the subsystems I/O relations. For large scale systems that can be hierarchially decomposed into groups of subsystems, sub-subsystems, sub-sub-subsystems, et cetera so that each group has relatively few interconnections with other groups, analysis is greatly facilitated: the result is applied successively to the various groups, beginning by determining stability and conic sector bounds for groups at the bottom of the hierarchy, then doing likewise for sub-subsystems, subsystems and so forth until stability and conic sector bounds have been determined for the complete interconnected system.

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