Multivariable Control

I General Topics.- 1 Applications of Algebraic Function Theory in Multivariable Control.- Preliminaries.- Classical Single-Loop Theory.- The Generalized Nyquist Stability Criterion.- Characteristic Gains and Fixed Modes.- Algebraic Functions and Riemann Surfaces.- The Riemann Surface Proof of the Generalised Nyquist Stability Criterion.- The Inverse Nyquist Stability Criterion and One-Parameter Families of Feedback Gains.- The Multivariab1e Root-Locus.- Poles and Zeros.- Approach and Departure Angles and Multivariab1e Pivots.- References.- 2 The Theory of Polynomial Combinants in the Context of Linear Systems.- Sets of Polynomials: Definitions and Normal Equivalence.- Almost Zeros: Definition Location and Computation.- Polynomial Combinants and the Exact and Approximate Zero Assignment Problems.- Strongly Nonassignab1e Sets and Almost Fixed Zeros.- Stability Aspects of Polynomial Combinants.- Conclusions.- References.- 3 The Occurrence of Non-Properness in Closed-Loop Systems and Some Implications.- Preliminary Observations.- Conditions for Closed-Loop Nonproperness.- Implications for Composite Systems.- Conclusions.- References.- 4 Skew-Symmetric Matrix Equations in Multivariable Control Theory.- Derivation of the Orthogonal Representation.- Skew-Symmetric Formulations.- Analytical Solutions in IR2x2 and IR3x3.- Analytical Solutions in IRnxn.- The Algebraic Riccati Generator.- Summary and Conclusions.- References.- 5 Feedback Controller Parameterizations: Finite Hidden Modes and Causality.- Main Results.- -Internal stability.- -Causality.- -Hidden Modes.- Conclusions.- References.- 6 Decompositions for General Multilinear Systems.- Time-Systems.- Linear and Multilinear Systems.- Decompositions for Multilinear Systems.- Conclusions.- References.- 7 Simplification of Models for Stability Analysis of Large-Scale Systems.- System Description and State-Space Representation.- Stability Analysis.- Application to the Definition of the Reduced Order System.- Algebraic Condition for the Application of the Results.- Methodology and Implementation.- Conclusion.- References.- II Uncertain Systems and Robust Control.- 8 Representations of Uncertainty and Robustness Tests for Multivariable Feedback Systems.- Representations of Uncertainty.- Robustness Tests.- Conclusions.- References.- 9 Additive,Multiplicative Perturbations and the Application of the Characteristic Locus Method.- Eigenvalue Inclusion Regions.- Stability and Design.- The Multiplicative Case.- A Robust Stability Study.- References.- 10 A Design Technique for Multi-Represented Linear Multi-Variable Discrete-Time Systems Using Diagonal or Full Dynamic Compensators.- Frequency Domain Bounds.- Choice of the Nominal Reference.- Realisation of the Compensator.- An Extension to Full Feedback Structures.- A Design Example.- References.- 11 Minimizing Conservativeness of Robustness Singular Values.- First and Second Derivatives of Singular Values.- Main Result.- Discussion.- Conclusions.- References.- III Algebraic and Optimal Controller Design.- 12 Frequency Assignment Problems in Linear Multivariable Systems:Exterior Algebra and Algebraic Geometry Methods.- Notation.- The Determinantal Pole,Zero Assignment Problems.- The Grassmann Representative of a Vector Space.- Plucker Matrices and the Linear Subproblem of DAP.- Decomposabi1ity of Multivectors: The Reduced Quadratic Plucker Relations.- Linearisation of the RQPRs and Feedback.- Conclusions.- References.- 13 On the Stable Exact Model Matching and Stable Minimal Design Problems.- Background.- Coprimeness in P of Proper and ?-Stable Rational Matrices.- Proper and ?-Stab1e,Minimal MacMillan Degree Bases of Rational Vector Spaces.- Stable Exact Model Matching and Stable Minimal Design Problems.- Conclusions.- References.- 14 Pole Placement in Discrete Multivariable Systems by Two and Three-Term Controllers.- Design of PID Controllers.- Design of PI Controllers.- Design of PD Controllers.- Conclusions.- References.- 15 Linear Quadratic Regulators with Prescribed Eigenvalues for a Family of Linear Systems.- Problem Formulation.- Sequential Pole Placement.- Example.- Application to Systems with Largely Varying Parameters.- Design Example.- Conclusions.- References.- 16 Sensitivity Reduction of the Linear Quadratic Optimal Regulator.- Sensitivity Reduction by Q Modification.- Extension for a Family of Plant Equations.- Conclusions.- References.- 17 Design of Low-Order Delayed Measurement Observers for Discrete Time Linear Systems.- Statement of the Problem.- Low-Order-Delayed Measurement Observer.- Example.- Conclusion.- References.- 18 Singular Perturbation Method and Reciprocal Transformation on Two-Time Scale Systems.- Presentation of the Singular Perturbations Method.- Definitions and Properties of the Reciprocal Transformation.- Resolution of a Singular Problem in Optimal Control by Reciprocal System.- Comparison on a Mechanical Example of Reduction Results Obtained by SP and (SP+R) Methods.- Conclusion.- References.- 19 Coordinated Decentralized Control with Multi-Model Representation (CODECO).- Tracking Approach to Coordinated Decentralized Control (CODECO).- Multimodel with Tracking Approach.- Algorithms Development.- Conclusion.- References.- 20 Design of Two-Level Optimal Regulators with Constrained Structures.- A Classification of Decomposition-Coordination Methods.- Principle of a New Method.- Application to Dynamic Processes.- Design of the First Leve1-Constrained Structures.- A Special Case for the Second Level:Disturbance Rejection.- Experiment Result.- Conclusion.- References.- IV Multidimensional Systems.- 21 A Canonical State-Space Model for m-Dimensional Discrete Systems.- m-D State-Space Model.- (m+l)-D State-Space Model.- Special Cases.- Example.- Conclusion.- References.- 22 Eigenvalue Assignment of 3-D Systems.- Problem Statement.- Problem Solution.- - Method 1.- - Method 2.- - Method 3.- References.- 23 Feedback Deadbeat Control of 2-Dimensional Systems.- Deadbeat Controller Design Using the Transfer Function Model.- Deadbeat Controller Design Using the State Space Model.- Example.- Appendices.- Conclusion.- References.- 24 State Observers for 2-D and 3-D Systems.- Observability and Controllability of 3-D Systems.- Transformation of Triangular 3-D Systems to Canonical Form.- The 2-D Parameter Identification Problem.- Identification via Model Reference Approachi:All States Accessible.- Adaptive Controller.- Adaptive Observer.- Description of 3-D State Observer.- State Observer Design for Triangular 3-D Systems.- Concluding Remarks.- References.- 25 Eigenvalue-Generalized Eigenvector Assignment Using PID Controller.- 1 - Continuous-time system.- Problem Statement.- Eigenvalue-Generalized Eigenvector Structure.- Numerical Examples.- 2 - Discrete-time system.- Problem Statement.- Eigenvalue-Generalized Eigenvector Assignment.- Illustrative Examples.- Conclusions.- References.