IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v100y1999i3d10.1023_a1022626120665.html
   My bibliography  Save this article

Robust Stability and Performance Analysis of Uncertain Systems Using Linear Matrix Inequalities

Author

Listed:
  • V. Balakrishnan

    (Purdue University)

  • R. L. Kashyap

    (Purdue University)

Abstract

A wide variety of problems in system and control theory can be formulated or reformulated as convex optimization problems involving linear matrix inequalities (LMIs), that is, constraints requiring an affine combination of symmetric matrices to be positive semidefinite. For a few very special cases, there are analytical solutions to these problems, but in general LMI problems can be solved numerically in a very efficient way. Thus, the reduction of a control problem to an optimization problem based on LMIs constitutes, in a sense, a solution to the original problem. The objective of this article is to provide a tutorial on the application of optimization based on LMIs to robust control problems. In the first part of the article, we provide a brief introduction to optimization based on LMIs. In the second part, we describe a specific example, that of the robust stability and performance analysis of uncertain systems, using LMI optimization.

Suggested Citation

  • V. Balakrishnan & R. L. Kashyap, 1999. "Robust Stability and Performance Analysis of Uncertain Systems Using Linear Matrix Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 100(3), pages 457-478, March.
    • Handle: RePEc:spr:joptap:v:100:y:1999:i:3:d:10.1023_a:1022626120665
    DOI: 10.1023/A:1022626120665
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1022626120665
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1022626120665?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Robert G. Bland & Donald Goldfarb & Michael J. Todd, 1981. "Feature Article—The Ellipsoid Method: A Survey," Operations Research, INFORMS, vol. 29(6), pages 1039-1091, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tanaka, Masato & Matsui, Tomomi, 2022. "Pseudo polynomial size LP formulation for calculating the least core value of weighted voting games," Mathematical Social Sciences, Elsevier, vol. 115(C), pages 47-51.
    2. Yaguang Yang, 2013. "A Polynomial Arc-Search Interior-Point Algorithm for Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 859-873, September.
    3. Zhang, Yufeng & Khani, Alireza, 2019. "An algorithm for reliable shortest path problem with travel time correlations," Transportation Research Part B: Methodological, Elsevier, vol. 121(C), pages 92-113.
    4. Paul Karaenke & Martin Bichler & Stefan Minner, 2019. "Coordination Is Hard: Electronic Auction Mechanisms for Increased Efficiency in Transportation Logistics," Management Science, INFORMS, vol. 65(12), pages 5884-5900, December.
    5. Simone A. Rocha & Thiago G. Mattos & Rodrigo T. N. Cardoso & Eduardo G. Silveira, 2022. "Applying Artificial Neural Networks and Nonlinear Optimization Techniques to Fault Location in Transmission Lines—Statistical Analysis," Energies, MDPI, vol. 15(11), pages 1-24, June.
    6. Robert M. Freund & Jorge R. Vera, 2009. "Equivalence of Convex Problem Geometry and Computational Complexity in the Separation Oracle Model," Mathematics of Operations Research, INFORMS, vol. 34(4), pages 869-879, November.
    7. Maxime C. Cohen & Ilan Lobel & Renato Paes Leme, 2020. "Feature-Based Dynamic Pricing," Management Science, INFORMS, vol. 66(11), pages 4921-4943, November.
    8. K. A. Ariyawansa & P. L. Jiang, 2000. "On Complexity of the Translational-Cut Algorithm for Convex Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 107(2), pages 223-243, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:100:y:1999:i:3:d:10.1023_a:1022626120665. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.