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Linear Matrix Inequalities in System and Control Theory

Linear Matrix Inequalities in System and Control Theory

Part of Studies in Applied and Numerical Mathematics

  • Date Published: December 1994
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Paperback
  • isbn: 9780898714852


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About the Authors
  • In this book the authors reduce a wide variety of problems arising in system and control theory to a handful of convex and quasiconvex optimization problems that involve linear matrix inequalities. These optimization problems can be solved using recently developed numerical algorithms that not only are polynomial-time but also work very well in practice; the reduction therefore can be considered a solution to the original problems. This book opens up an important new research area in which convex optimization is combined with system and control theory, resulting in the solution of a large number of previously unsolved problems.

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    Product details

    • Date Published: December 1994
    • format: Paperback
    • isbn: 9780898714852
    • length: 203 pages
    • dimensions: 255 x 180 x 15 mm
    • weight: 0.443kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    1. Introduction
    A Brief History of LMIs in Control Theory
    Notes on the Style of the Book
    Origin of the Book
    2. Some Standard Problems Involving LMIs. Linear Matrix Inequalities
    Some Standard Problems
    Ellipsoid Algorithm
    Interior-Point Methods
    Strict and Nonstrict LMIs
    Miscellaneous Results on Matrix Inequalities
    Some LMI Problems with Analytic Solutions
    3. Some Matrix Problems. Minimizing Condition Number by Scaling
    Minimizing Condition Number of a Positive-Definite Matrix
    Minimizing Norm by Scaling
    Rescaling a Matrix Positive-Definite
    Matrix Completion Problems
    Quadratic Approximation of a Polytopic Norm
    Ellipsoidal Approximation
    4. Linear Differential Inclusions. Differential Inclusions
    Some Specific LDIs
    Nonlinear System Analysis via LDIs
    5. Analysis of LDIs: State Properties. Quadratic Stability
    Invariant Ellipsoids
    6. Analysis of LDIs: Input/Output Properties. Input-to-State Properties
    State-to-Output Properties
    Input-to-Output Properties
    7. State-Feedback Synthesis for LDIs. Static State-Feedback Controllers
    State Properties
    Input-to-State Properties
    State-to-Output Properties
    Input-to-Output Properties
    Observer-Based Controllers for Nonlinear Systems
    8. Luré and Multiplier Methods. Analysis of Luré Systems
    Integral Quadratic Constraints
    Multipliers for Systems with Unknown Parameters
    9. Systems with Multiplicative Noise. Analysis of Systems with Multiplicative Noise
    State-Feedback Synthesis
    10. Miscellaneous Problems. Optimization over an Affine Family of Linear Systems
    Analysis of Systems with LTI Perturbations
    Positive Orthant Stabilizability
    Linear Systems with Delays
    Interpolation Problems
    The Inverse Problem of Optimal Control
    System Realization Problems
    Multi-Criterion LQG
    Nonconvex Multi-Criterion Quadratic Problems
    List of Acronyms

  • Authors

    Stephen Boyd

    Laurent El Ghaoul

    Eric Feron

    Venkataramanan Balakrishnan

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