Control of Linear Systems and
the Real Schubert Calculus
Mathematics Colloquium
University of California,
Santa Cruz
Frank Sottile
University of Wisconsin &
University of Massachusetts
26 October 1999
Control of Linear Systems and |
In 1981, Brockett and Byrnes showed how the static feedback laws which control a given linear system are determined through the Schubert calculus of enumerative geometry. This talk will describe that connection and propose numerical homotopy methods to solve the resulting systems of polynomial equations.
The related questions of finding real feedback laws and of trying to do Schubert's calculus over the real numbers are intertwined with a precise conjecture of Shapiro and Shapiro. We discuss a new result which shows it is possible to do Schubert's calculus over the real numbers and proves a version of this conjecture. In a similar vein, problems of enumerating rational curves in the Grassmannian (also known as quantum enumerative geometry) may also be solved over the real numbers.