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In this paper we propose a compositional scheme for the construction ofabstractions for networks of control systems using the interconnection matrixand joint dissipativity-type properties of subsystems and their abstractions.In the proposed framework, the abstraction, itself a control system (possiblywith a lower dimension), can be used as a substitution of the original systemin the controller design process. Moreover, we provide a procedure forconstructing abstractions of a class of nonlinear control systems by using thebounds on the slope of system nonlinearities. We illustrate the proposedresults on a network of linear control systems by constructing its abstractionin a compositional way without requiring any condition on the number or gainsof the subsystems. We use the abstraction as a substitute to synthesize acontroller enforcing a certain linear temporal logic specification. Thisexample particularly elucidates the effectiveness of dissipativity-typecompositional reasoning for large-scale systems.

Compositional abstraction for networks of control systems: A dissipativity approach