Positivity and storage functions for quadratic differential forms

Author

Trentelman, Harry L. ; Williems, J.C.

Author_Institution

Math. Inst., Groningen Univ., Netherlands

Volume

4

fYear

1996

fDate

11-13 Dec 1996

Firstpage

3964

Abstract

Differential equations and one-variable polynomial matrices play an essential role in describing dynamics of systems. When studying functions of the dynamical variables or specifying performance criteria in optimal control, we invariably encounter quadratic expressions in the variables and their derivatives. Two-variable polynomial matrices are the proper mathematical tool to express these quadratic functionals. We illustrate that dynamical equations expressed through one-variable polynomial matrices fit the functionals expressed through two-variable polynomial matrices

Keywords

differential equations; dynamics; observability; optimal control; polynomial matrices; differential equations; observability; optimal control; polynomial matrices; positivity; quadratic differential forms; quadratic functionals; storage functions; system dynamics; Artificial intelligence; Circuit theory; Counting circuits; Differential equations; Eigenvalues and eigenfunctions; Mathematics; Matrix decomposition; Optimal control; Polynomials; Symmetric matrices;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1996., Proceedings of the 35th IEEE Conference on

Conference_Location

Kobe

ISSN

0191-2216

Print_ISBN

0-7803-3590-2

Type

conf

DOI

10.1109/CDC.1996.577319

Filename

577319