ScholarLens Back to search
1986•IEEE Transactions on Automatic ControlRequires access

On the solution of a class of algebraic matrix Riccati equation

Charles Pearce

Open publisher page 9 citations

Abstract

We consider the algebraic matrix Riccati equation of control theory arising with a scalar control. It is shown that, if the Riccati equation is taken in phase-variable canonical form, the solution may be effected by solving a scalar polynomial equation whose degree is that of the unknown matrix. The resolution of the problem involves only elementary algebraic operations on the solution of the scalar polynomial equation. An illustrative numerical example is given.

About this research paper

What this paper is about

We consider the algebraic matrix Riccati equation of control theory arising with a scalar control. It is shown that, if the Riccati equation is taken in phase-variable canonical form, the solution may be effected by solving a scalar polynomial equation whose degree is that of the unknown matrix. The resolution of the problem involves only elementary algebraic operations on the solution of the scalar polynomial equation. An illustrative numerical example is given.

Why it matters

OpenAlex reports 9 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

We consider the algebraic matrix Riccati equation of control theory arising with a scalar control. It is shown that, if the Riccati equation is taken in phase-variable canonical form, the solution may be effected by solving a scalar polynomial equation whose degree is that of the unknown matrix. The resolution of the problem involves only elementary algebraic operations on the solution of the scalar polynomial equation. An illustrative numerical example is given.

Key concepts: Algebraic Riccati equation, Riccati equation, Mathematics, Matrix difference equation, Scalar (mathematics), Linear-quadratic regulator, Algebraic solution, Polynomial matrix

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
On the solution of a class of algebraic matrix Riccati equation — Research Paper | ScholarLens