Computing the distance between time-periodic dynamical systems

A recent generalization of Vinnicombe’s ν-gap metric accommodates linear time-varying (LTV) dynamics for a class of systems with graphs that admit normalized coprime representations. Such graph representations exist for systems generated by stabilizable and detectable LTV statespace models. In general, construction of normalized coprime representations is computationally challenging. In this paper, a numerical method for constructing normalized graph representations is provided for periodic state-space models. The construction involves the periodic solutions of corresponding periodic differential Riccati equations. Based on this, a bisection algorithm for computing the ν-gap metric is also provided.