Projective synchronization for two nonidentical time-delayed fractional-order T–S fuzzy neural networks based on mixed \({H_\infty }\)/passive adaptive sliding mode control

This paper deals with the problem of mixed \({H_\infty }\)/passive projective synchronization for two different fractional-order (FO) T–S fuzzy neural networks with uncertain parameters and time delays. Firstly, a fractional integral sliding surface which is suitable for the considered FO error system is proposed. Second, in terms of the established sliding surface, combining a novel reaching law, a new adaptive sliding mode control law is introduced, which can force the closed-loop dynamic error system trajectories to reach the sliding surface. Then, by giving a continuous frequency distributed model of the FO dynamic networks and the application of FO system stability theory, the projective synchronization conditions are addressed in terms of linear matrix inequality techniques. Based on the conditions, a desired controller which can guarantee the robust stability of the closed-loop system and also ensure a mixed \({H_\infty }\)/passive performance level is designed. Finally, synchronization of two nonidentical time-delayed FO T–S fuzzy neural networks with uncertain parameters as a simulation example is given to illustrate the effectiveness of the proposed method.