Friday December 10, 2010, 11.00-11.45, Room 3721, Lindstedtsv. 25

Amol Sasane Optimization and Systems Theory

The need for measuring the distance between control systems
is basic in control theory. For example, in robust control theory,
one knows that the unstable system P to be stabilized is just an
approximation of reality, and so one would really like the stabilizing
controller to not only stabilize the nominal system P, but also all
sufficiently close systems P' to P. The question of what one means
by "closeness" of systems thus arises naturally. So one needs a
metric on the set of unstable systems which is amenable to computation
and it has good properties in the robust stabilization problem.
Such a desirable metric was introduced by Glenn Vinnicombe in 1993,
and is called the ν-metric. There essentially the ring R of stable
transfer functions was taken to be the set of the rational functions
without poles in the closed unit disk. The problem of what happens when
R is some other ring of stable transfer functions was left open.
In this talk, we address this issue, and give an extension of the ν-metric.

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