Abstract
This chapter analyzes stability theory for countably infinite systems. It establishes new stability results for a class of countably infinite systems of ordinary differential equations. It considers those systems that may be viewed as an interconnection of countably many free or isolated subsystems (which are described by ordinary differential equations defined on finite dimensional spaces). Such systems are often called interconnected systems, composite systems, decentralized systems, large-scale systems, and the like. The objective in the chapter is to analyze interconnected systems in terms of their simpler subsystems and in terms of their interconnecting structure. An initial value problem for countably infinite systems of differential equations is analyzed. Interconnected systems are considered, and weak-coupling conditions are also analyzed.
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