STABILITY OF A NONLINEAR 2 DEGREE-OF-FREEDOM VEHICLE SYSTEM WITH MULTIPLE TIME-DELAYS

This paper examines dynamical behavior of a nonlinear oscillator which models a two-degree-of-freedom quarter-car forced by the road profile. We study the influence of multiple delays in the system, which is generally due to inherent dynamics of the actuator. This gives rise to delay differential equation (DDE) model of the system. Technical stability within definite time in Bogusz's sense for finite time domain is studied for different parameters. Asymptotic stability is derived and the effect of time-delay on the system is studied in detail. It is found that the asymptotic stability for t -> infinity becomes insufficient since we are interested in stability for finite time domain of the system's motion. The numerical results obtained are found to be in good agreement with analytical predictions.