Abstract

This paper proposes a projection neural network with delays, including discrete and distributed delay, for solving absolute value equations of the form Ax - |x| = b. By reformulating the absolute value equation as an equivalent optimization problem and exploiting the associated Karush-Kuhn- Tucker (KKT) conditions, the projection neural network model is systematically constructed. Sufficient conditions for global exponential convergence to a solution of the absolute value equation are derived using Lyapunov-Krasovskii functionals, novel integral inequalities, and linear matrix inequalities (LMIs) framework. Furthermore, three simulation examples are provided to demonstrate the effectiveness of the proposed approach under different conditions on ∥A-1∥, covering both ∥A-1∥ ≤ 1 and ∥A-1∥ > 1 cases, thereby extending existing neural network-based methods that primarily focus on the case ∥A-1∥ < 1.