Lur’e-Postnikov Lyapunov function approach to global robust Mittag-Leffler stability of fractional-order neural networks

Abstract

Abstract In this paper, the global robust Mittag-Leffler stability analysis is preformed for fractional-order neural networks (FNNs) with parameter uncertainties. A new inequality with respect to the Caputo derivative of integer-order integral function with the variable upper limit is developed. By means of the properties of Brouwer degree and the matrix inequality analysis technique, the proof of the existence and uniqueness of equilibrium point is given. By using integer-order integral with the variable upper limit, Lur’e-Postnikov type Lyapunov functional candidate is constructed to address the global robust Mittag-Leffler stability condition in terms of linear matrix inequalities (LMIs). Finally, two examples are provided to illustrate the validity of the theoretical results.

Keywords

• fractional-order neural networks
• global robust Mittag-Leffler stability
• Lur’e-Postnikov type Lyapunov functional
• Brouwer degree
• linear matrix inequality