On the existence of diagonal solutions to the Lyapunov equation for a third order system

Author

Oleng, Nicholas O. ; Narendra, Kumpati S.

Author_Institution

Dept. of Electr. Eng., Yale Univ., New Haven, CT, USA

Volume

3

fYear

2003

fDate

4-6 June 2003

Firstpage

2761

Abstract

An algebraic characterization of necessary and sufficient conditions for the existence of a diagonal solution P>0 to the Lyapunov equation for third order matrices has been derived. In this paper we show an alternative way of obtaining the same conditions. This is based on necessary and sufficient conditions that we derive for the existence of a common diagonal solution to the Lyapunov equation for two stable matrices in R^2×2. The importance of the new approach is that it appears to be possible to extend it to determine a common diagonal solution P>0 to the Lyapunov equation for two matrices A,B ∈ R^3×3 and even to more general cases.

Keywords

Lyapunov matrix equations; matrix algebra; stability; Lyapunov equation; diagonal solutions; diagonal stability; dynamical system; necessary conditions; sufficient conditions; third order matrices; third order system; Computer networks; Distributed control; Equations; Error correction; Error correction codes; Lyapunov method; Marine animals; Stability; Sufficient conditions; Symmetric matrices;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 2003. Proceedings of the 2003

ISSN

0743-1619

Print_ISBN

0-7803-7896-2

Type

conf

DOI

10.1109/ACC.2003.1243497

Filename

1243497