Performance Analysis of Time-Delay Systems under External Perturbations Using Output-to-Output Gain

What the math gives to ML

The paper provides a transferable dissipativity mechanism for quantifying how measurement and actuation delays amplify external perturbations: a delay-dependent Lyapunov–Krasovskii functional yields LMIs certifying an upper bound on output-to-output gain. The direct neural-network transfer is a delayed recurrent or state-space block whose local Jacobian is constrained by the same LMI, rather than relying only on zero-delay spectral-radius constraints. The certificate gives a measurable stability margin: increase the allowed delay until the LMI becomes infeasible, while monitoring the certified perturbation gain. A cheaper fixed-delay implementation uses Padé augmentation to convert delays into a finite-dimensional augmented state.