Upper solution bounds of the continuous and discrete coupled algebraic Riccati equations

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Davies, Richard, Shi, Peng and Wiltshire, Ron (2008) Upper solution bounds of the continuous and discrete coupled algebraic Riccati equations. Automatica, 44 (4). pp. 1088-1096. ISSN 0005-1098

Abstract

In this paper, we propose upper bounds for the sum of the maximal eigenvalues of the solutions of the continuous coupled algebraic Riccati equation (CCARE) and the discrete coupled algebraic Riccati equation (DCARE), which are then used to infer upper bounds for the maximal eigenvalues of the solutions of each Riccati equation. By utilizing the upper bounds for the maximal eigenvalues of each equation, we then derive upper matrix bounds for the solutions of the CCARE and DCARE. Following the development of each bound, an iterative algorithm is proposed which can be used to derive tighter upper matrix bounds. Finally, we give numerical examples to demonstrate the effectiveness of the proposed results, making comparisons with existing results.

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Item type	Article
URI	https://vuir.vu.edu.au/id/eprint/4752
DOI	10.1016/j.automatica.2007.11.001
Official URL	http://dx.doi.org/10.1016/j.automatica.2007.11.001
Subjects	Historical > Faculty/School/Research Centre/Department > Institute for Logistics and Supply Chain Management (ILSCM) Historical > FOR Classification > 0199 Other Mathematical Sciences Information Systems
Keywords	ResPubID18758, Coupled Riccati equation, jump linear systems, upper bounds, eigenvalues, JLQ problem, iterative algorithm
Citations in Scopus	27 - View on Scopus
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