Reduction of the small gain condition

The small gain condition is sufficient for ISS of interconnected systems. However, verification of the small gain condition requires large amount of computations in the case of a large size of the system. To facilitate this procedure we aggregate the subsystems and the gains between the subsystems that belong to certain interconnection patterns using three heuristic rules of aggregation. These rules keep the main structure of the mutual influences between the subsystems in the network. Furthermore, fulfillment of the reduced small gain condition implies ISS of the large network. Such reduction allows to decrease the number of computations needed to verify the small gain condition. An ISS-Lyapunov function for the large network can be constructed using the reduced small gain condition.

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