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Solution of some algebraic problems arising in the theory of stability and sensitivity of systems, with particular reference to the Lyapunov matrix equation

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posted on 2018-08-14, 13:21 authored by Stephen Barnett
The matrix equation A'P + PA = -Q arises when the direct method of Lyapunov is used to analyse the stability of a constant linear system of differential equations ẋ = Ax. Considerable attention is given to the solution of this equation for the symmetric matrix P, given a symmetric positive definite matrix Q. Several new methods are proposed, including a reduction in the number of equations and unknowns brought about by introducing a skew-symmetric matrix; a method based on putting A into Schwarz form and inverting a triangular matrix; and a solution in terms of a convergent infinite matrix series. Some numerical experience is also reported. [Continues.]

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  • Science

Department

  • Mathematical Sciences

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© Stephen Barnett

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

1967

Notes

A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.

Language

  • en

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