Asymptotic Stability Analysis And Stabilization Control Of Fractional-Order Vehicle Suspension System With Time Delay

Our study focuses on the analysis of asymptotic stability and the development of asymptotic stabilization control methods for fractional vehicle suspension systems (FVSS). We begin by constructing a mathematical model for FVSS using the state-space equations of Caputo fractional calculus. Initially, we utilize the fractional Routh–Hurwitz criterion to derive the necessary conditions for asymptotic stability and instability in the open-loop system of the fractional vehicle suspension. Subsequently, we propose a novel control strategy for FVSS and establish an associated asymptotic stabilization criterion by combining a new vector Lyapunov function with the M-matrix method. Moreover, we extend the fractional-order vehicle suspension model to include time delay resulting from the interactions between different variables in the real system, thus creating a FVSS with time delay. Based on the vector Lyapunov function, M-matrix measure, and Razumikhin interpretation, we develop a control strategy specifically tailored for FVSSs with time delay. Lastly, we compare two numerical simulations of the FVSS, one with time delay and one without, to demonstrate the accuracy, effectiveness, and applicability of the proposed method presented in our paper.