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In this paper, we develop a compositional scheme for the construction ofcontinuous approximations for interconnections of infinitely many discrete-timeswitched systems. An approximation (also known as abstraction) is itself acontinuous-space system, which can be used as a replacement of the original(also known as concrete) system in a controller design process. Having designeda controller for the abstract system, it is refined to a more detailed one forthe concrete system. We use the notion of so-called simulation functions toquantify the mismatch between the original system and its approximation. Inparticular, each subsystem in the concrete network and its corresponding one inthe abstract network are related through a notion of local simulationfunctions. We show that if the local simulation functions satisfy certainsmall-gain type conditions developed for a network containing infinitely manysubsystems, then the aggregation of the individual simulation functionsprovides an overall simulation function quantifying the error between theoverall abstraction network and the concrete one. In addition, we show that ourmethodology results in a scale-free compositional approach for anyfinite-but-arbitrarily large networks obtained from truncation of an infinitenetwork. We provide a systematic approach to construct local abstractions andsimulation functions for networks of linear switched systems. The requiredconditions are expressed in terms of linear matrix inequalities that can beefficiently computed. We illustrate the effectiveness of our approach throughan application to AC islanded microgirds.

Compositional Construction of Abstractions for Infinite Networks of Discrete-Time Switched Systems