Generic asymptotic error estimates for the numerical simulation of hybrid systems

We examine the convergence of discrete simulations for a large class of impulsive and hysteretic hybrid systems. We use a geometrically intuitive graph-distance metric on a suitable space of cadlag functions, then we develop strategies for constructing numerical approximate trajectories that converge generically (but not necessarily generally) to the exact trajectories. The original conjecture that the metric used here generates the Skorohod J1J1 topology was proved by Gokhman in [D. Gokhman, Topologies for hybrid solutions, J. Nonlinear Anal. Hybrid Systems 2 (2008) 468–473].