Stability Analysis of Time-varying Delay Neural Network for Convex Quadratic Programming With Equality Constraints and Inequality Constraints

The paper’s claimed stability condition matches a correct and standard route to global exponential stability for the projected delay system, but key steps in the paper’s proof are mathematically flawed or unjustified. In contrast, the candidate solution supplies a clean Halanay-inequality argument using the 1-Lipschitz property of the projection and the Lipschitz constant μ = ||I − αW||, which yields the desired estimate under the paper’s condition (|κ − 1| + 1)‖I − αW‖ − κ < 0. Specifically, the paper’s proof of Theorem 2 mishandles the projection nonlinearity and the delay term (e.g., it treats PU(u) − y* as PU(u − v), introduces spurious −αp terms that should cancel, and even writes an integral with a lower limit depending on the dummy variable, ∫_t−τ(s), which is invalid). These issues are visible around the variation-of-constants steps and subsequent inequalities for (15) and Theorem 2 in the PDF (see the formulation of (14)–(15), the stability condition statement, and the detailed inequalities in the proof) . The model’s solution does not rely on those faulty manipulations and delivers a complete, standard proof of global exponential stability.