Stability Analysis and Control of Repetitive Trajectory Systems in the State-Domain: Roller Coaster Application

This paper discusses the concepts of stability and asymptotic stability for state-dependent repetitive trajectory systems. An adaptive compensation method is proposed to compensate for disturbances that are a function of the system state. It will be shown that Lyapunov stability analysis can be performed in the state-domain if certain conditions are satisfied. The main theoretical contribution of the paper is to show that stability analysis can be carried out not only along the time axis but also in the state domain and that state-dependent disturbances or uncertainty can be successfully rejected. The motion dynamics of a roller coaster system is simulated to illustrate the practical importance of the proposed compensation method.