Mixed H _∞ and Passive Projective Synchronization for Fractional Order Memristor-Based Neural Networks with Time-Delay and Parameter Uncertainty

This paper investigates the mixed H _∞ and passive projective synchronization problem for fractional-order (FO) memristor-based neural networks. Our aim is to design a controller such that, though the unavoidable phenomena of time-delay and parameter uncertainty are fully considered, the resulting closed-loop system is asymptotically stable with a mixed H _∞ and passive performance level. By combining active and adaptive control methods, a novel hybrid control strategy is designed, which can guarantee the robust stability of the closed-loop system and also ensure a mixed H _∞ and passive performance level. Via the application of FO Lyapunov stability theory, the projective synchronization conditions are addressed in terms of linear matrix inequality techniques. Finally, two simulation examples are given to illustrate the effectiveness of the proposed method. (paper)