Upper solution bounds of the continuous and discrete coupled algebraic Riccati equations |
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Authors: | Richard Davies [Author Vitae] Peng Shi [Author Vitae]Author Vitae] |
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Affiliation: | Faculty of Advanced Technology, University of Glamorgan, Pontypridd CF37 1DL, UK |
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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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Keywords: | Coupled Riccati equation Jump linear systems Upper bounds Eigenvalues JLQ problem Iterative algorithm |
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