Fault Estimations and Non-Fragile Control Design for Fractional-Order Multi-Weighted Complex Dynamical Networks

Abstract

This paper deals with the robust fault estimation based synchronization problem for a class of fractional-order multi-weighted complex dynamic networks subject to external disturbances. Specifically, the synchronization problem is converted to an equivalent uniformly ultimately boundedness problem of the corresponding error system by use of spectral decomposition of the Laplacian and proper scalings of the faults. First, by introducing an intermediate estimator technique and using monochromatic Lyapunov function method, the sufficient condition for uniformly ultimately boundedness of the resulting error system via fault estimation based non-fragile controller is presented. Next, by using the linear matrix inequality (LMI) technique and optimization approach, the existence condition in the form of LMIs for designing the fault estimation based robust non-fragile controller is derived. Finally, two numerical examples including financial model are provided to demonstrate the validity and feasibility of the developed theoretical results.

Keywords

• Fractional-order complex dynamical networks
• multi-weights
• non-fragile control
• fault estimation