Fixed-Time Bipartite Synchronization of a Signed Graph: An Economical and Practical Strategy

A practical fixed-time control strategy is proposed for the bipartite synchronization of a signed graph. Under the assumption that the intrinsic function of isolated node is bounded, a fixed-time controller based on the exponential function is designed to avoid more parameters in most existing fixed-time methods. Compared with existing results, the proposed controllers not only relax the restriction that the intrinsic function is odd and satisfies Lipchitz condition, but also has the better convergence and the tighter bound of the settling time. Theoretical analyses on why the proposed controller has the higher convergence are given. Numerical experiments have verified the effectiveness, economy and practicability of the proposed strategy.