Synchronization for time-varying complex dynamical networks with different-dimensional nodes and non-dissipative coupling

This paper investigates synchronization for time-varying complex dynamical networks with different-dimensional nodes via decentralized control. The outer coupling configuration matrix (OCCM) in our network model, which represents the coupling strength and the topological structure, can be time-varying, non-dissipatively coupled, asymmetric and uncertain. In addition, the nonlinearly coupled inner state functions are admissible in the network model. The paper mainly focuses on the synthesis of decentralized controllers in two cases for uncertain coupling coefficients in OCCM, respectively. Firstly, the decentralized nonlinear state feedback controllers are synthesised based on the known coupling coefficients common bound. The proposed controllers can guarantee exponential synchronization of the networks. Then, an adaptive mechanism with only one parameter being adjusted online is introduced to synthesize the decentralized adaptive controllers according to the unknown coupling coefficients common bound so that the network realizes asymptotic synchronization. Finally, a numerical example is given to test the effectiveness of the theoretical results.