Nonlinear Vehicle Suspension with Multiple Delays: An Exponential Stability Study via the Razumikhin Technique
Abstract
This paper investigates the global exponential stability of a nonlinear quarte-car vehicle suspension model incorporating multiple, time-varying delays. We apply a general stability theorem for Second-order nonlinear delay differential equations (DDEs), leveraging the Razumikhin technique. A key feature of our analysis is the use of a Lyapunov function with a cross-term, which yields significantly less conservative stability conditions compared to existing results. We provide explicit criteria for parameter selection and derive a sharp estimate for the exponential delay rate. To demonstrate the practical applicability of our theoretical results, a numerical simulation is conducted in Python for a quarter-car model featuring nonlinear damping, cubic spring stiffness, and dual delayed feedback control. The simulation validates the derived stability bound and the calculated decay rate, confirming the method’s effectiveness for automotive engineering applications.
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