Cluster synchronization in nonlinear complex networks under sliding mode control

• Published in: Nonlinear dynamics Vol. 83; no. 1-2; pp. 739 - 749
• Main Authors: Hou, Huazhou, Zhang, Qingling, Zheng, Meng
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.01.2016; Springer Nature B.V
• Subjects: Automotive Engineering; Classical Mechanics; Clusters; Control; Differential calculus; Dynamical Systems; Engineering; Existence theorems; Linear matrix inequalities; Mathematical analysis; Matrix methods; Mechanical Engineering; Networks; Nonlinear dynamics; Nonlinear systems; Nonlinearity; Original Paper; Parameter uncertainty; Sliding mode control; Subsystems; Synchronism; Theorems; Uncertainty; Vibration; Cluster synchronization; Sliding mode control; Differential mean value theorem; Time-varying mismatched uncertainties
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-015-2363-z

This paper investigates the cluster synchronization for network of nonlinear systems via differential mean value theorem method and sliding mode control strategy. Because of the existence of the nonlinear dynamics, the differential mean value theorem method is used to transform the nonlinear error complex network system into a linear parameter-varying system. Since the robustness to the uncertainties of the sliding mode, we can deal with the linear parameter-varying system which contains the time-varying mismatched uncertainties by applying the sliding mode control strategy through the equivalent transformation. In addition, appropriate linear matrix inequality stability condition by the Lyapunov method is derived such that each subsystem in the new sliding mode is completely invariant to both matched and mismatched uncertainties. Finally, simulation example is shown to illustrate the effectiveness of the proposed method.