Continuity of singular perturbations in the graph topology

AbstractFor a certain model for singular perturbations in control systems, which we motivate by a simple example, we show that under weak assumptions continuity in the graph topology holds as the perturbation parameter tends to zero. This may be contrasted with a result by Cobb, who considered a different model for singular perturbations and who found a strong 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

A behavioral approach to singular systems

The notion of behaviors introduced by Willems gives a good description of dynamical systems without reference to any particular representation of the system in terms of equations. In this note, we introduce a notion of behaviors that allows us to describe singular systems in a very natural way. The new definition of behaviors given here is closely related to that of a sheaf over the projective line, and we make this connection precise

A behavioral approach to singular systems

The notion of behaviors introduced by Willems gives a good description of dynamical systems without reference to any particular representation of the system in terms of equations. In this note, we introduce a notion of behaviors that allows us to describe singular systems in a very natural way. The new definition of behaviors given here is closely related to that of a sheaf over the projective line, and we make this connection precise

Realization by inspection

We investigate which first-order representations can be obtained from high-order representations of linear systems `by inspection', that is just by rearrangement of the data. Under quite weak conditions it is possible to obtain minimal realizations in the so-called pencil form; under stronger conditions one can obtain minimal realizations in standard state space form by inspection. The development is based on a reformulation of the realization problem as a problem of finding a complete set of basis vectors for the nullspace of a given constant matrix. Since no numerical computation is needed, the realization method is in particular suitable for situations in which some of the coefficients are symbolic rather than numerical

A quantized current source with mesoscopic feedback

We study a mesoscopic circuit of two quantized current sources, realized by non-adiabatic single- electron pumps connected in series with a small micron-sized island in between. We find that quantum transport through the second pump can be locked onto the quantized current of the first one by a feedback due to charging of the mesoscopic island. This is confirmed by a measurement of the charge variation on the island using a nearby charge detector. Finally, the charge feedback signal clearly evidences loading into excited states of the dynamic quantum dot during single-electron pump operation