Resonance stability in electrical railway systems - A dissipativity approach

We propose a theory for stability analysis of railway systems based on energy exchange principles between the infrastructure and rolling stock. We show that if the rolling stock and infrastructure is dissipative with respect to specially constructed power functions (more general than voltage× current) stability is guaranteed. We thereby provide a proof of the Input Admittance Criterion (IAC) - a widely used empirical criterion in the railway industry - as special case of our results. Application of the theory is demonstrated with an example from a metro train system.