Stability analysis of “bridge–pedestrians” system based on Tsypkin criterion

A novelcybernetic model has been developed to analyzethe dynamics of the “bridge-pedestrians” system in the transverse direction, incorporating the functional state of the pedestrians. An analytical expression has been derived for the critical number of pedestrians capable of inducing rocking in the bridge. Additionally, the stability region of the system has been assessed using the frequency criterion established by Ya.Z. Tsypkin, specifically applied to the parameters of the London Millennium Bridge. The results of this study indicate that the rocking of the bridge may be attributed to a minor neuromuscular delay among pedestrians, rather than to the synchronization of their steps, as suggested in several existing publications. Furthermore, the obtained results may have broader implications for other classes of oscillatory human–machine systems.