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.
Highlights
Dynamical neural networks (DNNs) have been widely applied in all kinds of science and engineering fields, such as image and signal processing, pattern recognition, associative memory and combinational optimization, see [ – ]
In Refs. [ – ], the global robust stability conditions were presented for integer-order neural networks (INNs)
Motivated by the discussion above, in this paper, we investigate the global robust Mittag-Leffler stability for fractional-order neural networks (FNNs) with the interval uncertainties
Summary
Dynamical neural networks (DNNs) have been widely applied in all kinds of science and engineering fields, such as image and signal processing, pattern recognition, associative memory and combinational optimization, see [ – ]. [ – ], the global robust stability conditions were presented for integer-order neural networks (INNs). [ ] considered the global projective synchronization for FNNs and presented the Mittag-Leffler synchronization condition in terms of LMIs. In Ref.
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