Abstract:

We explore the interconnections between various ways of introducing the gap topology for linear time-invariant input/output systems. Specifically, we consider: (1) the topology defined by the gaps between the graphs of transfer functions (2) Vidyasagar's graph topology (3) the weakest topology in which the closed loop behavior of the standard feedback interconnection is continuous (4) the topology of uniform convergence of the associated Martin-Hermann mappings from $C^+$ to the Grassmannian manifold $Grass(m,m+p)$ ("pointwise gap") (5) the gap topology defined by the gaps between the associated $L^2(-\infty,0)$-behaviors. We also compare some different gap topologies.