A new numerical solution of $\\dot{X} = A_{1}X + XA_{2} + D, X(0) = C$

Author

Barraud, A.Y.

Author_Institution

Institut National Polytechnique de Grenoble, Grenoble, France

Volume

Issue

fYear

1977

fDate

12/1/1977 12:00:00 AM

Firstpage

976

Lastpage

977

Abstract

Another numerical solution of the general matrix differential equation $\\circ{X}=A_{1}X+XA_{2}+D, X(0)=C$ for X is considered without any stability condition for A1and A2. Like Davison\´s method, the proposed algorithm requires only some n2words of memory and $n_{3}$ multiplications where $n=\\max (n_{1},n_{2})$ and $A \\in R^{n_{1} \\times n_{1}},A_{2} \\in R^{n_{2} \\times n_{2}}$ . This new approach is well suited to solve large and possibly unstable systems. We take the opportunity to run the differential equation for various D. A very efficient technique follows to design the so-called receding horizon control problem.

Keywords

Differential equations; Matrix equations; Numerical integration; Control systems; Differential equations; Eigenvalues and eigenfunctions; Erbium; Matrices; Open loop systems; Stability;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.1977.1101634

Filename

1101634

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=825260