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Title: Solution of some algebraic problems arising in the theory of stability and sensitivity of systems, with particular reference to the Lyapunov matrix equation
Author: Barnett, Stephen
Awarding Body: Loughborough University of Technology
Current Institution: Loughborough University
Date of Award: 1967
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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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available