Quasi-stability and quasi-synchronization control of quaternion-valued fractional-order discrete-time memristive neural networks

Abstract A discrete-time fractional-order quaternion-valued memristive system is considered in this note. By utilizing contraction mapping theory, a sufficient condition for the existence and uniqueness of the equilibrium point for the considered system is derived. Via the comparison principle of linear fractional difference system, the quasi-stability condition of the given system is obtained, subsequently, the quasi-synchronization conclusion is derived through Lyapunov method and a proper controller, which can well handle the quasi-synchronization problem in the process of implementing the controller. Applying the lexicographical order method to the quaternion-valued memristive neural networks, the closed convex hull consisted by the connection weights is meaningful. One example is given to substantiate the obtained conclusions.

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