In control theory we often wish to find a feedback control $u$ to stabilize a given linear system $\dot{x} = A x + B u, y= Cx$. The problem of linear adaptive control consists in constructing such a controller, using measurements of $y$ only, without precise a priori knowledge about the matrices $A$, $B$, and $C$.
During the 1970s and 1980s several adaptive control algorithms appeared, under restrictive assumptions on the matrices. Notably the transfer function $c (sI - A)^{-1}b$, in the single-input, single-output case, was required to be minimum-phase (have stable zeroes). It was thought that some of those assumptions were indeed necessary.
In 1986 Bengt Mårtensson in his Lund PhD thesis "Adaptive Stabilization" showed that essentially all one needs to know are the dimensions of the matrices. For effective practical algorithms of course more a priori information is crucial. This discovery of "universal stabilizers" came as a great surprise to the adaptive control community. The techniques used, involving switching and dense search, were also rather unexpected.
