Robust Control of Linear Dynamical Systems

Robust Control of Linear Dynamical Systems

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Since the mid-1980s, significant advances have taken place in the area of robust control. Often, however, original ideas and the motivations for pursuing a particular path have been lost in a maze of mathematical formalism. This work is intended to bring these ideas and techniques to the attention of a wider audience. The author uses a step-by-step approach to guide the reader through this sometimes difficult material. Mathematical rigour is balanced with readability to provide the reader with a straightforward understanding of the important aspects of robust control. The book is suitable as a textbook for students with some previous exposure to linear system theory. It is equally appropriate for self study for those interested in acquiring a deeper knowledge of robust control design.
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Product details

  • Hardback | 383 pages
  • 159 x 235 x 27mm | 645g
  • Academic Press Inc
  • San Diego, United States
  • English
  • 66ill.
  • 0121678857
  • 9780121678852

Table of contents

Background and motivation: what is robust control?; historical perspective; models and modelling; model reduction. Introduction to robust control: elements of robust control theory; design objectives and specifications; shaping the loop gain; Signals and systems: signals and their norms; computation of H2 norm; computation of H, H norm and associated algebraic relationship; all-pass systems, the adjoint operator; inverse systems. Matrix fraction description: factorization of polynomial matrices; testing for coprimeness; rational functions - matrix fraction description; the Smith-McMillan form, factorization over a ring of stable matrices; coprime fractional representation in state space. Parametrization of stabilizing controllers: well posedness and internal stability; the Youla parametrization approach; co-prime factorization in state space revisited; strong stabilization; Sensitivity minimization and robust stabilization: sensitivity minimization; 1-block, 2-block, and 4-block problems; sensitivity trade-offs for multivariable plants; design limitations due to R.H. plane zeros; plant uncertainty and robustness; robust stabilizing controllers. Balanced realization and Hankel norm approximation: balanced realization; best approximation in Hilbert space; the Hankel operator; the Hankel norm approximation problem; Glover's method. H2 and H optimization: LQG methodology; H optimization techniques; the Nevanlinna-Pick interpolation problem; operator-theoretic methods. Generalised plan-controller configuration: the standard configuration; stabilizability criteria; parametrization of stabilizing controllers for G22; reduction to the standard problem; from standard form to model matching. Controller synthesis in state space: LQG control-full information problem; the Kalman filter; parametrization of output feedback controllers. (Part contents).
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