Hamiltonian indices and rational spectral densitiesSeveral (global) topological properties of various spaces of linear systems, particularly symmetric, lossless, and Hamiltonian systems, and multivariable spectral densities of fixed McMillan degree are announced. The study is motivated by a result asserting that on a connected but not simply connected manifold, it is not possible to find a vector field having a sink as its only critical point. In the scalar case, this is illustrated by showing that only on the space of McMillan degree = /Cauchy index/ = n, scalar transfer functions can one define a globally convergent vector field. This result holds both in discrete-time and for the nonautonomous case. With these motivations in mind, theorems of Bochner and Fogarty are used in showing that spaces of transfer functions defined by symmetry conditions are, in fact, smooth algebraic manifolds.
Document ID
19820042047
Acquisition Source
Legacy CDMS
Document Type
Conference Proceedings
Authors
Byrnes, C. I. (Harvard University Cambridge, MA, United States)
Duncan, T. E. (Harvard University Cambridge, MA; Kansas, University, Lawrence, KS, United States)