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Polynomial Methods for Control Systems Design
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Table of Contents

Preface ix.- 1 A Tutorial on H2 Control Theory: The Continuous Time Case.- 1.1 Introduction.- 1.2 LQG control theory.- 1.2.1 Problem formulation.- 1.2.2 Finite horizon solution.- 1.2.3 Infinite horizon solution.- 1.3 H2 control theory.- 1.3.1 Preliminaries.- 1.3.2 State space solution.- 1.3.3 Wiener-Hopf solution.- 1.3.4 Diophantine equations solution.- 1.4 Comparison and examples.- 1.4.1 The LQG as an H2 problem.- 1.4.2 Internal stability.- 1.4.3 Solvability assumptions.- 1.4.4 Non-proper plants.- 1.4.5 Design examples.- 1.5 References.- 2 Frequency Domain Solution of the Standard H? Problem.- 2.1 Introduction.- 2.1.1 Introduction.- 2.1.2 Problem formulation.- 2.1.3 Polynomial matrix fraction representations.- 2.1.4 Outline.- 2.2 Well-posedness and closed-loop stability.- 2.2.1 Introduction.- 2.2.2 Well-posedness.- 2.2.3 Closed-loop stability.- 2.2.4 Redefinition of the standard problem.- 2.3 Lower bound.- 2.3.1 Introduction.- 2.3.2 Lower bound.- 2.3.3 Examples.- 2.3.4 Polynomial formulas.- 2.4 Sublevel solutions.- 2.4.1 Introduction.- 2.4.2 The basic inequality.- 2.4.3 Spectral factorization.- 2.4.4 All sublevel solutions.- 2.4.5 Polynomial formulas.- 2.5 Canonical spectral factorizations.- 2.5.1 Definition.- 2.5.2 Polynomial formulation of the rational factorization.- 2.5.3 Zeros on the imaginary axis.- 2.6 Stability.- 2.6.1 Introduction.- 2.6.2 All stabilizing sublevel compensators.- 2.6.3 Search procedure - Type A and Type B optimal solutions.- 2.7 Factorization algorithm.- 2.7.1 Introduction.- 2.7.2 State space algorithm.- 2.7.3 Noncanonical factorizations.- 2.8 Optimal solutions.- 2.8.1 Introduction.- 2.8.2 All optimal compensators.- 2.8.3 Examples.- 2.9 Conclusions.- 2.10 Appendix: Proofs for section 2.3.- 2.11 Appendix: Proofs for section 2.4.- 2.12 Appendix: Proof of theorem 2.7.- 2.13 Appendix: Proof of the equalizing property.- 2.14 References.- 3 LQG Multivariable Regulation and Tracking Problems for General System Configurations.- 3.1 Introduction.- 3.2 Regulation problem.- 3.2.1 Problem solution.- 3.2.2 Connection with the Wiener-Hopf solution.- 3.2.3 Innovations representations.- 3.2.4 Relationships with other polynomial solutions.- 3.3 Tracking, servo and accessible disturbance problems.- 3.3.1 Problem formulation.- 3.4 Conclusions.- 3.5 Appendix.- 3.6 References.- 4 A Game Theory Polynomial Solution to the H? Control Problem.- 4.1 Abstract.- 4.2 Introduction.- 4.3 Problem definition.- 4.4 The game problem.- 4.4.1 Main result.- 4.4.2 Summary of the simplified solution procedure.- 4.4.3 Comments.- 4.5 Relations to the J-factorization H? problem.- 4.5.1 Introduction.- 4.5.2 The J-factorization solution.- 4.5.3 Connection with the game solution.- 4.6 Relations to the minimum entropy control problem.- 4.7 A design example: mixed sensitivity.- 4.7.1 Mixed sensitivity problem formulation.- 4.7.2 Numerical example.- 4.8 Conclusions.- 4.9 Appendix.- 4.10 References.- 4.11 Acknowledgements.- 5 H2 Design of Nominal and Robust Discrete Time Filters.- 5.1 Abstract.- 5.2 Introduction.- 5.2.1 Digital communications: a challenging application area...- 5.2.2 Remarks on the notation.- 5.3 Wiener filter design based on polynomial equations.- 5.3.1 A general H2 filtering problem.- 5.3.2 A structured problem formulation.- 5.3.3 Multisignal deconvolution.- 5.3.4 Decision feedback equalizers.- 5.4 Design of robust filters in input-output form.- 5.4.1 Approaches to robust H2 estimation.- 5.4.2 The averaged H2 estimation problem.- 5.4.3 Parameterization of the extended design model.- 5.4.4 Obtaining error models.- 5.4.5 Covariance matrices for the stochastic coefficients.- 5.4.6 Design of the cautious Wiener filter.- 5.5 Robust H2 filter design.- 5.5.1 Series expansion.- 5.5.2 The robust linear state estimator.- 5.6 Parameter tracking.- 5.7 Acknowledgement.- 5.8 References.- 6 Polynomial Solution of H2 and H? Optimal Control Problems with Application to Coordinate Measuring Machines.- 6.1 Abstract.- 6.2 Introduction.- 6.3 H.2 control design.- 6.3.1 System model.- 6.3.2 Assumptions.- 6.3.3 The H2 cost function.- 6.3.4 Dynamic weightings.- 6.3.5 The H2 controller.- 6.3.6 Properties of the controller.- 6.3.7 Design procedure.- 6.4 H? Robust control problem.- 6.4.1 Generalised H2 and H? controllers.- 6.5 System and disturbance modelling.- 6.5.1 System modelling.- 6.5.2 Disturbance modelling.- 6.5.3 Overall system model.- 6.6 Simulation and experimental studies.- 6.6.1 System definition.- 6.6.2 Simulation studies.- 6.6.3 Experimental studies.- 6.6.4 H? control.- 6.7 Conclusions.- 6.8 Acknowledgements.- 6.9 References.- 6.10 Appendix: two-DOF H2 optimal control problem.

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