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Design of Fixed-Order Stabilizing and \(\mathcal{H}_2\) - \(\mathcal{H}_\infty\) Optimal Controllers: An Eigenvalue Optimization Approach

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Time Delay Systems: Methods, Applications and New Trends

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 423))

Abstract

An overview is presented of control design methods for linear time-delay systems, which are grounded in numerical linear algebra techniques such as large-scale eigenvalue computations, solving Lyapunov equations and eigenvalue optimization. The methods are particularly suitable for the design of controllers with a prescribed structure or order. The analysis problems concern the computation of stability determining characteristic roots and the computation of \(\mathcal{H}_2\) and \(\mathcal{H}_{\infty}\) type cost functions. The corresponding synthesis problems are solved by a direct optimization of stability, robustness and performance measures as a function of the controller parameters.

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Authors and Affiliations

  1. Department of Computer Science, K.U. Leuven, Celestijnenlaan 200A, 3001, Heverlee, Belgium

    Wim Michiels

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  1. Wim Michiels
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Correspondence to Wim Michiels .

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Editors and Affiliations

  1. Dept. Mechanical Engineering, Northeastern University, Huntingdon Ave. 360, Boston, 02115, Massachusetts, USA

    Rifat Sipahi

  2. Technicka Street 4, Prague, 166 07, Czech Republic

    Tomáš Vyhlídal

  3. , CNRSSupélec, L2S (UMR CNRS 8506), rue Joliot Curie 3, Gif-sur-Yvette, 91192, France

    Silviu-Iulian Niculescu

  4. , Department of Electrical and Information, University of L’Aquila, Via G. Gronchi 18, L’Aquila, 67100, Italy

    Pierdomenico Pepe

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Michiels, W. (2012). Design of Fixed-Order Stabilizing and \(\mathcal{H}_2\) - \(\mathcal{H}_\infty\) Optimal Controllers: An Eigenvalue Optimization Approach. In: Sipahi, R., Vyhlídal, T., Niculescu, SI., Pepe, P. (eds) Time Delay Systems: Methods, Applications and New Trends. Lecture Notes in Control and Information Sciences, vol 423. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25221-1_15

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  • DOI: https://doi.org/10.1007/978-3-642-25221-1_15

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  • Publisher Name: Springer, Berlin, Heidelberg

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  • Online ISBN: 978-3-642-25221-1

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