Non-separation method-based robust finite-time synchronization of uncertain fractional-order quaternion-valued neural networks

Abstract

In this paper, robust finite-time synchronization (F-TS) issue is addressed for a class of uncertain fractional-order quaternion-valued neural networks by employing non-separation method instead of separation method. First, a general fractional differential inequality is developed to provide new insight into the research about finite-time stability and synchronization of fractional-order systems. Next, quaternion-valued feedback controller and quaternion-valued adaptive controller are designed. On the basis of the newly developed inequality, quaternion inequality techniques, together with the properties of fractional calculus and reduction to absurdity, some easily-verified algebraic criteria for robust F-TS are established, and the settling time for robust F-TS is explicitly reckoned, which depends on not only the controller parameters but also the initial values and order of the considered systems. Eventually, numerical results are provided to substantiate our robust F-TS criteria.