A recursive solution to the suboptimal block Nehari problem

David Leroy Augenstein, Purdue University

Abstract

In this thesis, a recursive, inverse scattering solution to the suboptimal block Nehari problem is developed for discrete systems by using two approaches which generalize the classical Levinson and Schur Algorithms used in signal processing. In the first approach, contractive matrix extension techniques are employed together with realization theory. The recursion equations that are developed reduce in the scalar case to the classical Schur Algorithm. The second approach develops a generalized Levinson Algorithm that is used with realization theory to derive a Nehari solution via positive definite matrix extensions. The two approaches arrive at equivalent sets of recursion equations that are valid for both forward and inverse scattering with strictly contractive block Hankel matrices. With these results, the set of all solutions to the suboptimal block Nehari problem is parameterized by an infinite sequence of contractions. The Nehari solution that corresponds to all of the contractions equalling zero will be characterized in terms of a discrete minimal realization and the associated controllability and observability grammians. Finally, by expanding on results of Foias-Frazho, state space representations of all solutions to the suboptimal block Nehari problem are developed.

Degree

Ph.D.

Advisors

Frazho, Purdue University.

Subject Area

Aerospace materials|Electrical engineering|Mechanical engineering

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