Stability analysis of time-varying delay neural network system utilizing free-matrix-based double integral inequality

In this paper, we propose two free-matrix-based double integral inequality. Unlike the generally widely used double integral inequalities, it provides a convex-type estimation and guarantees a tighter upper bound than the existing integral inequality by using information about the state as well as the state derivative. In addition, a less conservative stability criterion on time-varying delay neural network system is derived using the proposed double integral inequality. We evaluate the superiority of the proposed free matrix-based double integral inequality through well-known numerical example.