Use this URL to cite or link to this record in EThOS: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.446089
Title: Bounds for the solution of algebraic matrix equations arising in mathematical control theory
Author: Davies, Richard
ISNI:       0000 0001 2418 202X
Awarding Body: University of Glamorgan
Current Institution: University of South Wales
Date of Award: 2007
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Abstract:
The study of solution bounds of algebraic Lyapunov and Riccati equations are highly important in control problems, and have been an attractive research topic over the past three decades. The solution bounds give solution estimates, and can also be applied to solve such problems involving these equations, hence a motivation for the research attraction. Besides, in control applications involving them, the exact solutions are often not required, but rather bounds of their solution, particularly when solving the equation is difficult. Therefore, many papers have proposed solution bounds for these equations, mainly for a deterministic nominal system, when the exact values of the coefficient matrices of the equations are available. Additionally, some works have focused on solution bounds of these equations for perturbed systems, when only approximate values of the coefficient matrices are available, so they available are perturbed versions of their actual values; as a consequence of these perturbed coefficient matrices, the solution matrix also becomes perturbed, so it becomes of interest to estimate the disturbance range for the solution. Furthermore, fewer works have focused on solution bounds of coupled algebraic Lyapunov and Riccati equations arising from stochastic systems, for both nominal and perturbed cases. In fact, it appears that there is no paper in the literature that studies solution bounds of perturbed coupled algebraic Riccati equations. Finally, many existing bounds only exist under assumptions which are not always valid, many of which are not realistic in control problems involving each equation. Furthermore, some bounds do not appear to be as tight as others, some bounds require heavy and complicated calculations to determine, and some are not very concise. Therefore, this work seeks to obtain solution bounds for Lyapunov and Riccati equations, which are tighter, less restrictive, possibly simpler in calculation, and more concise than existing results. When possible, all derived results shall be compared with existing results to verify the advantage(s) of the new results.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.446089  DOI: Not available
Keywords: control theory
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