Feedback control of linear systems and 
       the real Schubert calculus

           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.