CONTINUITY OF SINGULAR PERTURBATIONS IN THE GRAPH TOPOLOGY

For a certain model for singular perturbations in control systems, whi ch we motivate by a simple example, we show that under weak assumption s continuity in the graph topology holds as the perturbation parameter tends to zero. This may be contrasted with a result by Cobb, who cons idered a different model for singular perturbations and who found a st rong condition to be necessary for continuity in that model. Our proof techniques are based on the characterization (due to Qiu and Davison) of the graph topology as a topology of uniform convergence.