In this paper, synchronization for a class of uncertain fractional-order neural networks subject to external disturbances and disturbed system parameters is studied. Based on the fractional-order extension of the Lyapunov stability criterion, an adaptive synchronization controller is designed, and fractional-order adaptation law is proposed to update the controller parameter online. The proposed controller can guarantee that the synchronization errors between two uncertain fractional-order neural networks converge to zero asymptotically. By using some proposed lemmas, the quadratic Lyapunov functions are employed in the stability analysis. Finally, numerical simulations are presented to confirm the effectiveness of the proposed method.

The present paper attempts to investigate the problem of robust H ${}_{\infty }$ control for a class of uncertain singular neutral time-delay systems. First, a linear matrix inequality (LMI) is proposed to give a generalized asymptotically stability condition and an H ${}_{\infty }$ norm condition for singular neutral time-delay systems. Second, the LMI is utilized to solve the robust H ${}_{\infty }$ problem for singular neutral time-delay systems, and a state feedback control law verifies the solution. Finally, four theorems are formulated in terms of a matrix equation and linear matrix inequalities.