Comparison principles and stability of nonlinear fractional-order cellular neural networks with multiple time delays

Some comparison principles for fractional-order linear systems with multiple time delays are established, after Mittag–Leffler functions are showed to be positive. Then by the stability theory of fractional linear delayed systems, the comparison system with multiple time delays is showed to be asymptotically stable under some conditions. Based on the comparison results, the asymptotical stability of the original systems follows from that of the comparison system. Then the obtained results are applied to investigate the asymptotical stability of nonlinear fractional-order cellular neural networks with multiple time delays. In terms of the inequality satisfied by the fractional derivative of Lyapunov function, some criteria ensuring asymptotical stability of fractional neural models are derived. Numerical simulations are presented to demonstrate the validity and feasibility of the proposed stability criteria.