Linear robust control - Green, Michael; Limebeer, David J. N. (Mineola, N.Y. : Dover Publications, Incorporated, 2012)
"Recent years have witnessed enormous strides in the field of robust control of dynamical systems-- unfortunately, many of these developments have only been accessible to a small group of experts. In this text for students and control engineers, the authors examines all of these advances, providing an in-depth and exhaustive examination of modern optimal and robust control. "--Provided by publisher.
Contents Preface 1 Introduction 1.1 Goals and origins of H optimal control 1.2 Optimizing the command response 1.3 Optimal disturbance attenuation 1.3.1 Internal stability theory for stable plants 1.3.2 Solution of the disturbance attenuation problem 1.4 A robust stability problem 1.5 Concluding comments and references 1.6 Problems 2 Multivariable Frequency Response Design 2.1 Introduction 2.2 Singular values 2.2.1 The singular value decomposition 2.2.2 Singular value inequalities 2.3 Singular values and the sensitivity operator. 2.4 Robust stability analysis2.4.1 A Nyquist stability theorem 2.4.2 Additive model error 2.4.3 Multiplicative model error 2.4.4 Examples 2.5 Performance analysis and enhancement 2.5.1 Disturbance attenuation 2.5.2 Tracking 2.5.3 Sensor errors 2.5.4 The control signal 2.5.5 Robust performance 2.5.6 Analytic limits on performance 2.6 Example 2.7 Notes and References 2.8 Problems 3 Signals and Systems 3.1 Signals 3.1.1 The size of signals 3.1.2 Signals in the frequency domain 3.2 Systems 3.2.1 Linear systems 3.2.2 The space L 3.2.3 The space H 3.2.4 Adjoint systems. 3.2.5 Allpass systems3.3 The size of a system 3.3.1 The incremental gain 3.3.2 The induced norm 3.3.3 The 2-norm of a system 3.4 The small gain theorem 3.5 Loop transformation 3.5.1 Multipliers or weights 3.5.2 Linear shift 3.5.3 Passivity 3.6 Robust stability revisited 3.7 The bounded real lemma 3.7.1 An algebraic proof 3.7.2 An optimal control proof 3.8 Notes and References 3.9 Problems 4 Linear Fractional Transformations 4.1 Introduction 4.1.1 The composition formula 4.1.2 Interconnections of state-space LFTs 4.2 LFTs in controller synthesis. 4.2.1 The generalized regulator problem4.2.2 The full-information problem 4.3 Contractive LFTs 4.3.1 Constant matrix case 4.3.2 Dynamic matrix case 4.4 Minimizing the norm of constant LFTs 4.5 Simplifying constant LFTs 4.6 Simplifying the generalized plant 4.7 Notes and References 4.8 Problems 5 LQG Control 5.1 Introduction 5.2 Full information 5.2.1 The finite-horizon case 5.2.2 The infinite-horizon case 5.2.3 Inclusion of cross terms 5.3 The Kalman filter 5.3.1 The finite-horizon case 5.3.2 The infinite-horizon case 5.4 Measurement feedback 5.4.1 The finite-horizon case. 5.4.2 The infinite-horizon case5.5 Notes and References 5.6 Problems 6 Full-Information H Controller Synthesis 6.1 Introduction 6.2 The finite-horizon case 6.2.1 Connection to differential games 6.2.2 First-order necessary conditions 6.2.3 The Riccati equation 6.2.4 Sufficiency: completing the square 6.2.5 Necessity 6.2.6 All closed-loop systems 6.2.7 All controllers 6.3 The infinite-horizon case 6.3.1 Preliminary observations 6.3.2 Sufficiency 6.3.3 A monotonicity property 6.3.4 Assumptions 6.3.5 Necessity 6.3.6 All controllers 6.4 Notes and References 6.5 Problems.
Originally published: Englewood Cliffs, N.J. : Prentice Hall, c1995.
Includes bibliographical references (pages 507-523) and index.
Keywords: Linear control systems; Linear systems