Distributed delayed impulsive control for μ-synchronization of multi-link structure networks with bounded uncertainties and time-varying delays of unmeasured bounds: A novel Halanay impulsive inequality approach

This study discusses the μ−synchronization of multi-link structure networks with parameter uncertainties and nonlinear couplings. Three types of variable delays, including internal, coupling, and distributed delays at sampling moments are deliberated in the synchronization control process. Different from existing multi-link models, the bulk of delays can be non-differentiable and unmeasured, which also brings new challenges to our research. To conquer the difficulties caused by such multiple generalized time delays, a novel Halanay-like impulsive inequality is established by utilizing the properties of μ−function and mathematical induction recipes. For letting the multi-link networks achieve μ−synchronization, a distributed-delay impulsive controller is designed, and multiple coupling matrices are decomposed into diagonal matrices and residual matrices. Based on the stability function method, the derived impulsive inequality, and matrix decomposition techniques, important synchronization conditions for the concerning multi-link networks are obtained, which releases the traditional constraints that delays should be smaller than impulsive intervals, and popularizes the existing synchronization results respecting multi-link systems with unbounded delays.