Linear Matrix Inequalities in System and Control Theory (Studies in Applied and Numerical Mathematics v. 15)

Linear Matrix Inequalities in System and Control Theory (Studies in Applied and Numerical Mathematics v. 15)

By: Stephen Boyd (author), Eric Feron (author), Venkataramanan Balakrishnan (author), Laurent El Ghaoul (author)Paperback

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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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Preface; 1. Introduction; Overview; 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. Lure and Multiplier Methods. Analysis of Lure 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; Notation; List of Acronyms; Bibliography; Index.

Product Details

  • publication date: 01/01/1987
  • ISBN13: 9780898714852
  • Format: Paperback
  • Number Of Pages: 203
  • ID: 9780898714852
  • weight: 443
  • ISBN10: 0898714850

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