M. S. Ravi's Research

Research Interests:

  • My research interests are twofold: understanding the defining equations of algebraic varieties, and applications of algebraic geometry to systems and control theory. I have pursued the second interest, for the most part, in collaboration with Joachim Rosenthal and Xiaochang Wang . My interests in systems theory has also led me to dabble in quantum cohomology of the Grassmanian, and its applications to the interpolation theory of rational matrix functions.

    Publications

    1. Regularity of Ideals and Their Radicals, Manuscripta Mathematica, Vol. 68 (1990), pp. 77-87.
    2. An Effective Version of Nori's Theorem, Math Zeitschrift, Vol. 214 (1993), pp. 1-8.
    3. Determinantal Equations for Secant Varieties of Curves, Communications in Algebra, Vol. 22, No.8 (1994) pp. 3103-3106.
    4. (with J. Rosenthal) A smooth compactification of the space of transfer functions with fixed McMillan degree. Acta Appl. Math, 34:329-352, 1994.
    5. (with J. Rosenthal, and X. Wang) On generic stabilizability and pole assignability. Systems & Control Letters, 23(2):79-84, 1994.
    6. (with J. Rosenthal) A general realization theory for higher order linear differential equations. Systems & Control Letters, 25(5):351-360, 1995.
    7. (with J. Rosenthal, and X. Wang) On decentralized dynamic pole placement and feedback stabilization. IEEE Trans. Automat. Contr., 40(9):1603-1614, 1995.
    8. Coordinate Rings of G/P are Koszul, J.of Algebra, Vol. 177, pp.367-371, 1995.
    9. (with J. Rosenthal, and X. Wang) Dynamic pole assignment and Schubert calculus. SIAM J. Control Optim., 34(3):813-832, 1996.
    10. Geometric Methods in Rational Interpolation Theory, Linear Algebra and its Applications, 258:159-168, 1997.
    11. (with J. Rosenthal and J. M. Schumacher) Homogeneous Behaviors, Mathematics of Control, Signals and Systems, 10: 61-75, 1997.
    12. (with Luc Habets) Reachability and stabilizability of systems over polynomial rings and a related genericity result", Proceedings of 3rd European Control Conference, Rome, 1995, pp. 224 - 229.
    13. (with J. Rosenthal, and X. Wang) Degree of the generalized Plücker embedding of a quot scheme and quantum cohomology, Math. Ann., 311, 11-26, 1998.
    14. (with V.  Lomadze, J. Rosenthal and J. M. Schumacher) A behavioral approach to singular systems, Acta Appl. Math, 54: pp. 331-344, 1998.
    15. Interpolation Theory and Quantum Cohomology, SIAM J. Control Optim., 39(3):pp. 981-988, 2000.( pdf file )
    16. (with J. Rosenthal, and Uwe Helmke) Output Feedback invariants, pdf file, Linear Algebra and its Applications, 351-352:pp. 623-637, 2002.