Fixed/Prescribed-time synchronization of multi-layer complex networks under switching control

The fixed/preassigned time (FT/PT) synchronization issue of multi -layer networks via a discontinuous control strategy is addressed in this paper. Firstly, the inventiveness FT theorem is established, and a precise estimation of setting time is given by employing mathematical induction, proof by contradiction, and maximum value theory. Subsequently, based on the FT stability results, several FT synchronization criteria for multilayer networks are proposed by designing a periodically switching protocol. Additionally, the topological connectivity constraints are eliminated through the implementation of synchronized states as virtual nodes. Correspondingly, the PT synchronization issue is investigated by developing several extraordinary control strategies in which the control gains are finite. Ultimately, the feasibility of the developed control design and the established criteria is illustrated by two numerical examples.