LAUSR

This paper gives the stability analysis of Filippov system with delay. Under the Filippov‐framework, we introduce a general type of Lyapunov‐Krasovskii functional (LKF) to derive the stability of delayed differential inclusions (DDIs), where the indefiniteness or positive definiteness of the derivative of LKF holds for almost everywhere along the trajectories of state solution. The proposed LKF of this paper generalizes the classic LKF whose derivative possesses negative definiteness or seminegative definiteness for everywhere. As a result, the stability, uniform stability, uniform asymptotic stability, and global exponential stability criteria of the trivial solution for DDI are established. Moreover, the developed LKF method is applied to solve the stabilization control issue of delayed neural networks, possessing discontinuous input‐output activation.