Stabilizability of multivariable systems and the Ljusternik-Snirel'mann category of real Grassmannians (Q760396)

The problem of stabilization (or, more generally, pole-shifting) by static output feedback has attracted a considerable amount of nontrivial and very nice mathematics, of which this paper is an example. The goal is to find the function, say b(m,p), such that b(m,p) is the largest integer n for which it is known that (generically) systems of dimension n and m inputs, p outputs, can be stabilized. It is known that \(mp\geq b(m,p)\geq m+p\)-1, but very little else in that generality. Based on algebraic geometric calculations, better (but difficult to calculate) bounds are given in this paper. For example, it is shown as a corollary of more general results, that b(2,6)\(\geq 9\).