Ron Wiltshire

Publications (3)1.03 Total impact

• Article: New lower matrix bounds for the solution of the continuous algebraic lyapunov equation

  Richard Davies, Peng Shi, Ron Wiltshire
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  ABSTRACT: New lower matrix bounds are derived for the solution of the continuous algebraic Lyapunov equation (CALE). Following each bound derivation, an iterative algorithm is proposed to derive tighter matrix bounds. In comparison to existing results, the presented results are more concise and are always valid when the CALE has a non-negative definite solution. We finally give numerical examples to show the effectiveness of the derived bounds and make comparisons with existing results. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society
  Asian Journal of Control 08/2008; 10(4):449 - 455. · 1.03 Impact Factor
• Article: Upper solution bounds of the continuous and discrete coupled algebraic Riccati equations

  Richard Davies, Peng Shi, Ron Wiltshire
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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.
  Automatica.
• Article: New upper solution bounds of the discrete algebraic Riccati matrix equation

  Richard Davies, Peng Shi, Ron Wiltshire
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  ABSTRACT: In this note, we present upper matrix bounds for the solution of the discrete algebraic Riccati equation (DARE). Using the matrix bound of Theorem 2.2, we then give several eigenvalue upper bounds for the solution of the DARE and make comparisons with existing results. The advantage of our results over existing upper bounds is that the new upper bounds of Theorem 2.2 and Corollary 2.1 are always calculated if the stabilizing solution of the DARE exists, whilst all existing upper matrix bounds might not be calculated because they have been derived under stronger conditions. Finally, we give numerical examples to demonstrate the effectiveness of the derived results.
  Journal of Computational and Applied Mathematics.