Feedback control of linear systems and the real Schubert calculus Santa Clara University Mathematics Colloquium Frank Sottile MSRI 27 October 1998

In 1981, Brockett and Byrnes showed how the 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 polynomials.

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 will discuss this connection and present some partial results and computational evidence in support of this conjecture.