AbstractThe problems of exponential quasi‐stabilization of quaternion‐valued memristive networks are further studied in this article. Different from the common Lyapunov function method in the literature, where the conclusions are derived based on the algebraic inequality, in this article, a novel norm (Frobenius norm) is constructed by using the Lyapunov function, which avoid breaking the integrity of the system. In addition, the Frobenius norm are applied to derive new quasi‐stabilization conditions. Less conservative results are obtained since the Frobenius norm contains more system information. Examples demonstrate the correctness of the developed new results.