Multivariable Control

1. Front Matter

   Pages i-xxii

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2. General Topics

   1. Front Matter

      Pages 1-1

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   2. Applications of Algebraic Function Theory in Multivariable Control

      • M. C. Smith

      Pages 3-26

   3. The Theory of Polynomial Combinants in the Context of Linear Systems

      • C. Giannakopoulos, N. Karcanias, G. Kalogelopoulos

      Pages 27-41

   4. The Occurrence of Non-Properness in Closed-Loop Systems and Some Implications

      • A. C. Pugh

      Pages 43-63

   5. Skew-Symmetric Matrix Equations in Multivariable Control Theory

      • F. C. Incertis

      Pages 65-84

   6. Feedback Controller Parameterizations: Finite Hidden Modes and Causality

      • P. J. Antsaklis, M. K. Sain

      Pages 85-104

   7. Decompositions for General Multilinear Systems

      • Paulo A. S. Veloso

      Pages 105-123

   8. Simplification of Models for Stability Analysis of Large-Scale Systems

      • I. Zambettakis, J. P. Richard, F. Rotella

      Pages 125-148

3. Uncertain Systems and Robust Control

   1. Front Matter

      Pages 149-149

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   2. Representations of Uncertainty and Robustness Tests for Multivariable Feedback Systems

      • Ian Postlethwaite, Yung Kuan Foo

      Pages 151-160

   3. Additive, Multiplicative Perturbations and the Application of the Characteristic Locus Method

      • R. W. Daniel, B. Kouvaritakis

      Pages 161-178

   4. A Design Technique for Multi-Represented Linear Multi-Variable Discrete-Time Systems Using Diagonal or Full Dynamic Compensators

      • Nicos M. Christodoulakis

      Pages 179-196

   5. Minimizing Conservativeness of Robustness Singular Values

      • Michael G. Safonov, John C. Doyle

      Pages 197-207

4. Algebraic and Optimal Controller Design

   1. Front Matter

      Pages 209-209

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   2. Frequency Assignment Problems in Linear Multivariable Systems: Exterior Algebra and Algebraic Geometry Methods

      • N. Karcanias, C. Giannakopoulos

      Pages 211-232

   3. On the Stable Exact Model Matching and Stable Minimal Design Problems

      • Antonis I. G. Vardulakis, Nicos Karcanias

      Pages 233-263

   4. Pole Placement in Discrete Multivariable Systems by Two and Three-Term Controllers

      • H. Seraji

      Pages 265-279

   5. Linear Quadratic Regulators with Prescribed Eigenvalues for a Family of Linear Systems

      • F. Heger, P. M. Frank

      Pages 281-292

   6. Sensitivity Reduction of the Linear Quadratic Optimal Regulator

      • C. Verde, P. M. Frank

      Pages 293-306

The foundation of linear systems theory goes back to Newton and has been followed over the years by many improvements such as linear operator theory, Laplace Transformation etc. After the World War II, feedback control theory has shown a rapid development, and standard elegant analysis and synthesis techniques have been discovered by control system workers, such as root-locus (Evans) and frequency response methods (Nyquist, Bode). These permitted a fast and efficient analysis of simple-loop control systems, but in their original "paper-and-pencil" form were not appropriate for multiple­ loop high-order systems. The advent of fast digital computers, together with the development of multivariable multi-loop system techniques, have eliminated these difficulties. Multivariable control theory has followed two main avenues; the optimal control approach, and the algebraic and frequency-domain control approach. An important key concept in the whole multivariable system theory is "ob­ servability and controllability" which revealed the exact relationships between transfer functions and the state variable representations. This has given new insight into the phenomenon of "hidden oscillations" and to the transfer function modelling of dynamic systems. The basic tool in optimal control theory is the celebrated matrix Riccati differential equation which provides the time-varying feedback gains in a linear-quadratic control system cell. Much theory presently exists for the characteristic properties and solution of this Riccati equation.

• Generator
• algebra
• design
• development
• model
• optimal control
• system

• Electrical Engineering Department, University of Patras, Patras, Greece

  Spyros G. Tzafestas

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