Periodic Solutions and Exponential Stability of Nonlinear Neutral Differential Systems with State-Dependent Delays via Matrix Measure Approach

This paper investigates a class of nonlinear neutral functional differential systems with multiple state-dependent delays. By combining the matrix measure framework with Banach’s and Krasnoselskii’s fixed point principles, we derive new explicit and verifiable criteria for the existence and uniqueness of T-periodic solutions. Furthermore, we establish sufficient conditions for the exponential stability of the unique periodic solution, showing how the strength of the linear dissipation competes with the sensitivity of the state-dependent delays. The proposed results extend and unify several earlier contributions on systems with constant or time-varying delays, and rigorously characterize the influence of nonlinear feedback-dependent delay terms on periodic dynamics. Three detailed numerical examples are presented to verify the sharpness and applicability of the obtained conditions.