Exponential synchronization and state estimation of inertial quaternion-valued Cohen-Grossberg neural networks: Lexicographical order method

This paper addresses the problems of synchronization and state estimation for a class of inertial quaternion-valued Cohen-Grossberg neural networks. By means of proper control strategy, sufficient conditions are derived for ascertaining exponential synchronization of quaternion-valued Cohen-Grossberg neural networks. Subsequently, the state estimation problem has also been augmented to achieve robust stable performance of the estimation error system. What should be mentioned is that, the system states considered in this paper are taking values in an interval, which implies that the states are varying between two different quaternions, thus, an optimal algorithm (lexicographical order method) is employed, which can be used to determine the "magnitude" of two different quaternions. In this case, the interval proposed by the quaternion-valued is meaningful. Finally, numerical examples are provided to demonstrate the effectiveness of the derived theoretical results.