Lur’e Postnikov Lyapunov functional technique to global Mittag-Leffler stability of fractional-order neural networks with piecewise constant argument

Abstract

Abstract In this paper, the global Mittag-Leffler stability issue of fractional-order neural networks (FNNs) with piecewise constant argument is investigated. Firstly, a new inequality with respect to the fractional derivative of integer-order variable upper limit integral is proposed, which not only is favorable to the construction of Lyapunov function but also enriches the fractional order calculus theory. Secondly, based on topological degree theory, the existence and uniqueness of equilibrium point is certified. In addition, under some suitable assumptions, by applying Picard successive approximation technique, the proof of the existence and uniqueness of solution with the initial value is given. Moreover, by introducing integral term into Lyapunov functional, Lur’e Postnikov type Lyapunov functional is constructed, and a sufficient condition is addressed in terms of linear matrix inequalities (LMIs) to guarantee that the considered FNNs are Mittag-Leffler stable. Finally, an example is given to demonstrate the validity of the obtained results.