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Mathematics Colloquium: Reachability and Holdability of Nonnegative States
4:10 pm Neill 5W
Abstract: We will discuss recent developments and open problems regarding linear differential systems dx/dt=Ax(t) whose solutions become and remain nonnegative. We will see that the eigenvalue of A furthest to the right must be real and must possess nonnegative right and left eigenvectors. Moreover, for some nonnegative number a, A+aI must be eventually nonnegative, namely, its powers must become and remain entrywise nonnegative. Applications to linear control theory will be presented.