Pole Placement, Internal Stabilization and Interpolation Conditions for Rational Matrix Functions: A Grassmannian Formulation
The problem of pole placement via dynamic feedback and the bitangential interpolation problem are shown to be both particular instances of a general subspace interpolation problem formulated for rational curves from projective space into a Grass-mannian manifold. The problem of determining the minimal degree d for an interpolant in terms of the problem data is shown to be computable via intersection theory in projective space. Using the projective dimension theorem bounds for the minimal degree interpolant curve are given.
Key wordsMultivariable Systems Interpolation Problems Dynamic Feedback Compensation Autoregressive Systems
Unable to display preview. Download preview PDF.
- A.C. Antoulas and J.C. Willems, A basis-free approach to linear exact modeling, preprint.Google Scholar
- J.A. Ball and J.W. Helton, Lie groups over the field of rational functions, signed spectral factorization, signed interpolation and amplifier design, J. Operator Theory, 9 (1982), 1964.Google Scholar
- J.A. Ball, I. Gohberg and L. Rodman, “Sensitivity minimization and bitangential Nevanlinna-Pick interpolation in contour integral form,” in Signal Processing II: Control Theory and Applications (ed. F.A. Grünbaum et al), IMA Vol. in Math, and its Appl. Vol. 23, Springer-Verlag, (1990), pp. 3–35.Google Scholar