Vibration distribution in complex dynamical systems: Local topology design for global performance?

Most of the results in complex dynamical systems are associated with collective properties such as synchronization, flocking, and consensus etc. The important problem of vibration distribution among the networks has not been paid enough attention. This vibration distribution problem is attacked in this paper with the concept of local design for global performance. Fundamental issues such as solution existence, solution uniqueness, feasible solutions, and optimal design synthesis are addressed. The important results are approached within a geometric design framework, which allows the performance to be visualized, facilitating the designer to approach the limit of performance without iterative or optimization algorithmic routines. The claims are validated through numerical examples and real-time simulations. (C) 2020 Published by Elsevier Ltd.