Green M., Limebeer D.J.N., Linear Robust Control

London, Pearson Education, 560 pages.Goals and origins of H∞ optimal control.
Optimizing the command response.
Optimal disturbance attenuation.
Internal stability theory for stable plants.
Solution of the disturbance attenuation problem.
A robust stability problem.
Concluding comments and references.
Problems.
Multivariable Frequency Response Design.Singular values.
The singular value decomposition.
Singular value inequalities.
Singular values and the sensitivity operator.
Robust stability analysis.
A Nyquist stability theorem.
Additive model error.
Multiplicative model error.
Examples.
Performance analysis and enhancement.
Disturbance attenuation.
Tracking.
Sensor errors.
The control signal.
Robust performance.
Analytic limits on performance.
Example.
Notes and References.
Problems.
Signals and Systems.
Signals.
The size of signals.
Signals in the frequency domain.
Systems.
Linear systems.
The space L∞.
The space H∞.
Adjoint systems.
Allpass systems.
The size of a system.
The incremental gain.
The induced norm.
The 2-norm of a system.
The small gain theorem.
Loop transformation.
Multipliers or weights.
Linear shift.
Passivity.
Robust stability revisited.
The bounded real lemma.
An algebraic proof.
An optimal control proof.
Notes and References.
Problems.
Linear Fractional Transformations.The composition formula.
Interconnections of state-space LFTs.
LFTs in controller synthesis.
The generalized regulator problem.
The full-information problem.
Contractive LFTs.
Constant matrix case.
Dynamic matrix case.
Minimizing the norm of constant LFTs.
Simplifying constant LFTs.
Simplifying the generalized plant.
Notes and References.
Problems.
LQG Control.Full information.
The finite-horizon case.
The infinite-horizon case.
Inclusion of cross terms.
The Kalman filter.
The finite-horizon case.
The infinite-horizon case.
Measurement feedback.
The finite-horizon case.
The infinite-horizon case.
Notes and References.
Problems.
Full-Information H∞ Controller Synthesis.The finite-horizon case.
Connection to differential games.
First-order necessary conditions.
The Riccati equation.
Sufficiency: completing the square.
Necessity.
All closed-loop systems.
All controllers.
The infinite-horizon case.
Preliminary observations.
Sufficiency.
A monotonicity property.
Assumptions.
Necessity.
All controllers.
Notes and References.
Problems.
The H∞ Filter.Finite-horizon results.
Necessary and sufficient conditions.
All solutions.
Terminal state estimation properties.
Infinite-horizon results.
viii CONTENTS.
The H∞ Wiener filtering problem.
Example: Inertial navigation system.
Notes and References.
Problems.
The H∞ Generalized Regulator Problem.Problem statement.
Finite-horizon results.
Two necessary conditions.
Necessary and sufficient conditions.
Infinite-horizon results.
A necessary condition.
An equivalent problem.
Necessary and sufficient conditions.
Example.
Notes and References.
Problems.
Model Reduction by Truncation.State-space truncation.
The truncation error.
Singular perturbation approximation.
Balanced realization.
Model reduction motivation.
Balanced realization.
Balanced truncation.
Stability.
Error bound for “one-step” truncation.
The error bound for balanced truncation.
Balanced singular perturbation approximation.
Example.
Notes and References.
Problems.
Optimal Model Reduction.Hankel operators.
The Hankel norm.
Hankel singular values and the Schmidt decomposition.
A lower bound on the approximation error.
Suboptimal Hankel norm approximations.
Allpass embedding.
CONTENTS ix.
One solution to the model reduction problem.
All solutions to the model reduction problem.
Optimal Hankel norm approximation.
Optimal allpass embedding.
One optimal Hankel norm approximant.
All optimal approximants.
Nehari’s theorem.
The infinity norm error bound.
Hankel singular values of optimal error systems.
The error bound.
Example.
Notes and References.
Problems.
The Four-Block Problem.The constant matrix problem.
Suboptimal solutions.
The necessary conditions.
State-space construction of the dilation.
The sufficient conditions.
Frequency weighted model reduction.
Problem formulation and a lower bound.
Reformulation as a four-block problem.
Allpass dilation.
Infinity norm error bounds.
Relative error model reduction.
Example.
All H∞ optimal controllers.
Notes and References.
Problems.
Design Case Studies.Robust stability.
Normalized coprime factor perturbations.
Loop-shaping design procedure.
Tokamak plasma control.
The system model.
The design problem.
Control system design.
Antiwindup scheme.
Bumpless transfer scheme.
Simulations.
x CONTENTS.
High-purity distillation.
Design specification.
The system model.
Two-degree-of-freedom controller design.
Design weight selection.
Simulation results.
Notes and References.
Appendices.
A Internal Stability Theory.
A.1 Introduction.
A.1.1 Basics.
A.2 Coprime factorization.
A.2.1 Coprime factorization and internal stability.
A.2.2 Doubly coprime factorization.
A.3 All stabilizing controllers.
A.4 Internal stability of LFTs.
A.4.1 The full-information configuration.
A.5 Notes and References.
A.6 Problems.
B Discrete-Time H∞ Synthesis Theory.
B.1 Introduction.
B.1.1 Definitions.
B.1.2 Problem statement.
B.2 Full information.
B.2.1 Finite horizon.
B.2.2 Infinite horizon.
B.2.3 Convergence of the Riccati equation.
B.3 Filtering.
B.3.1 Finite horizon.
B.3.2 Infinite horizon.
B.4 Measurement feedback.
B.4.1 Finite horizon.
B.4.2 Infinite horizon.
B.5 Notes and References.
B.6 Problems.