Asymptotic behaviour of the solution of the projection Riccati differential equation

Author

Callier, Frank M. ; Winkin, Joseph J.

Author_Institution

Dept. of Math., Facultes Univ. Notre-Dame de la Paix, Namur, Belgium

Volume

41

Issue

5

fYear

1996

fDate

5/1/1996 12:00:00 AM

Firstpage

646

Lastpage

659

Abstract

The solution of the Riccati differential equation (RDE) is shown to be asymptotically close to the solution of the projection Riccati differential equation (PRDE). The asymptotic behaviour of the latter is analyzed in an explicit formula. The almost-periodic asymptote of the solution of the PRDE is computed by an algorithm based upon the concepts of an aperiodic/almost-periodic generator (APG) decomposition of a linear map and unit row-staircase form of a polynomial matrix. The analysis ultimately provides a convergence criterion. In particular, it is shown that the solution of the PRDE always converges in the aperiodic case

Keywords

Riccati equations; convergence of numerical methods; eigenvalues and eigenfunctions; nonlinear differential equations; polynomial matrices; almost-periodic generator; aperiodic generator; asymptotic behaviour; convergence; decomposition; eigenvalues; linear map; polynomial matrix; projection Riccati differential equation; Associate members; Control systems; Differential equations; Eigenvalues and eigenfunctions; H infinity control; Helium; Matrix decomposition; Optimal control; Polynomials; Riccati equations;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.489202

Filename

489202