NEW RESULTS IN POLE ASSIGNMENT BY REAL OUTPUT-FEEDBACK

This paper considers the problem of turning natural frequencies of a linear system by a memoryless controller. Using algebro-geometric methods it is shown how it is possible to improve current sufficiency conditions. The main result is an exact combinatorial characterization of the nilpotency index of the mod 2 cohomology ring of the real Grassmannian. Using this characterization, new sufficiency results for generic pole assignment for the linear system with m-inputs, p-outputs, and McMillan degree n are given. Among other results it is shown that 2.25 . max(m, p) + min(m, p) - 3 greater-than-or-equal-to n is a sufficient condition for generic real pole placement, provided min(m, p) greater-than-or-equal-to 4.