Preface Glossary I Dynamical Systems 1 Nonlinear Systems--Fundamentals and Examples 1.1 State Space Models 1.1.1 Notational Conventions 1.1.2 Rescaling 1.1.3 Comparison Functions 1.
2 Control Loops, Controller Design, and Examples 1.2.1 The Pendulum on a Cart 1.2.2 Mobile Robots--The Nonholonomic Integrator 1.3 Exercises 1.4 Bibliographical Notes and Further Reading 2 Nonlinear Systems--Stability Notions 2.1 Stability Notions 2.
1.1 Local versus Global Properties 2.1.2 Time-Varying Systems 2.2 Comparison Principle 2.3 Stability by Lyapunov''s Second Method 2.3.1 Time-Varying Systems 2.
3.2 Instability 2.3.3 Partial Convergence and the LaSalle-Yoshizawa Theorem 2.4 Region of Attraction 2.5 Converse Theorems 2.5.1 Stability 2.
6 Invariance Theorems 2.6.1 Krasovskii-LaSalle Invariance Theorem 2.6.2 Matrosov''s Theorem 2.7 Exercises 2.8 Bibliographical Notes and Further Reading 3 Linear Systems and Linearization 3.1 Linear Systems Review 3.
1.1 Stability Properties for Linear Systems 3.1.2 Quadratic Lyapunov Functions 3.2 Linearization 3.3 Time-Varying Systems 3.4 Numerical calculation of Lyapunov functions 3.4.
1 Linear Matrix Inequalities and Semidefinite Programming 3.4.2 Global Lyapunov Functions for Polynomial Systems 3.4.3 Local Lyapunov Functions for Polynomial Systems 3.4.4 Estimation of the Region of Attraction 3.5 Systems with Inputs 3.
5.1 Controllability and Observability 3.5.2 Stabilizability and Detectability 3.5.3 Pole Placement 3.6 Exercises 3.7 Bibliographical Notes and Further Reading 4 Frequency Domain Analysis 4.
1 Fundamental Results in the Frequency Domain 4.1.1 The Laplace Transform 4.1.2 The Transfer Function 4.1.3 The 2-, â- and â-norm 4.2 Stability Analysis in the Frequency Domain 4.
2.1 Bounded-Input, Bounded-Output Stability 4.2.2 System Interconnections in the Frequency Domain 4.2.3 The Bode Plot 4.2.4 The Nyquist Criterion 4.
3 Exercises 4.4 Bibliographical Notes and Further Reading 5 Discrete Time Systems 5.1 Discrete Time Systems--Fundamentals 5.2 Sampling: From Continuous to Discrete Time 5.2.1 Discretization of Linear Systems 5.2.2 Higher Order Discretization Schemes 5.
3 Stability Notions 5.3.1 Lyapunov Characterizations 5.3.2 Linear Systems 5.3.3 Stability Preservation of Discretized Systems 5.4 Controllability and Observability 5.
5 Exercises 5.6 Bibliographical Notes and Further Reading 6 Absolute Stability 6.1 A Commonly Ignored Design Issue 6.2 Historical Perspective on the Lur''e Problem 6.3 Sufficient Conditions for Absolute Stability 6.3.1 Circle Criterion 6.3.
2 Popov Criterion 6.3.3 Circle versus Popov Criterion 6.4 Exercises 6.5 Bibliographical Notes and Further Reading 7 Input-to-State Stability 7.1 Motivation and Definition 7.2 Lyapunov Characterizations 7.3 System Interconnections 7.
3.1 Cascade Connections 7.3.2 Feedback Interconnections 7.4 Integral-to-Integral Estimates and 2-Gain 7.4.1 System interconnections 7.5 Integral ISS and Nonlinear 2-Gain 7.
6 Dissipativity and Passivity 7.7 Exercises 7.8 Bibliographical Notes and Further Reading II Controller Design 8 LMI-Based Controller and Antiwindup Designs 8.1 2-Gain Optimization for Linear Systems 8.1.1 Asymptotic Stability and 2-Gain Optimization 8.1.2 Feedback Synthesis 8.
2 Systems with Saturation 8.2.1 LMI-Based Saturated Linear State Feedback Design 8.2.2 Global Asymptotic Stability Analysis 8.2.32-Stability and 2-Gain Optimization 8.3 Regional Analysis 8.
3.1 Local Asymptotic Stability 8.3.22-Stability and 2-Gain Optimization 8.4 Antiwindup Synthesis 8.4.1 Global Antiwindup Synthesis 8.4.
2 Well-Posedness of the Control Law 8.4.3 Regional Antiwindup Synthesis 8.5 Exercises 8.6 Bibliographical Notes and Further Reading 9 Control Lyapunov Functions 9.1 Control Affine Systems 9.2 ISS Redesign via LgV Damping 9.3 Sontag''s Universal Formula 9.
4 Backstepping 9.4.1 Avoiding Cancellations 9.4.2 Exact Backstepping and a High-Gain Alternative 9.4.3 Convergence Structure 9.5 Forwarding 9.
5.1 Forwarding mod LgV 9.5.2 Convergence Structure 9.5.3 Saturated Control 9.6 Stabilizability and Control Lyapunov Functions 9.6.
1 Existence of Lipschitz Continuous Feedback Laws 9.6.2 Nonsmooth Control Lyapunov Functions 9.6.3 Robustness and Discontinuous Feedback Laws 9.7 Exercises 9.8 Bibliographical Notes and Further Reading 10 Sliding Mode Control 10.1 Finite-Time Stability 10.
2 Basic Sliding Mode Control 10.2.1 Terminology 10.2.2 Chattering and Chattering Avoidance 10.3 A More General Structure 10.4 Estimating the Disturbance 10.5 Output Tracking 10.
6 Exercises 10.7 Bibliographical Notes and Further Reading 11 Adaptive Control 11.1 Motivating Examples and Challenges 11.1.1 Limitations of Static Feedback Laws 11.1.2 Estimation-Based Controller Designs 11.2 Model Reference Adaptive Control 11.
3 Adaptive Control for Nonlinear Systems 11.3.1 Adaptive Backstepping 11.3.2 Tuning Function Designs 11.3.3 Application: Single Link Manipulator with Flexible Joint 11.4 Exercises 11.
5 Bibliographical Notes and Further Reading 12 Introduction to Differential Geometric Methods 12.1 Introductory Examples 12.2 Zero Dynamics and Relative Degree 12.3 Feedback Linearization 12.3.1 Nonlinear Controllability 12.3.2 Input-to-State Linearization 12.
4 Exercises 12.5 Bibliographical Notes and Further Reading 13 Output Regulation 13.1 Linear Output Regulation 13.2 Robust Linear Output Regulation 13.3 Nonlinear Output Regulation 13.4 Exercises 13.5 Bibliographical Notes and Further Reading 14 Optimal Control 14.1 Optimal Control--Continuous Time Setting 14.
1.1 Linear Quadratic Regulator 14.1.2 Control-Affine Nonlinear Systems 14.1.3 Inverse Optimality 14.2 Optimal Control--Discrete Time Setting 14.2.
1 Definitions and Notations 14.2.2 The Linear Quadratic Regulator 14.3 From Infinite- to Finite-Dimensional Optimization 14.3.1 The Principle of Optimality 14.3.2 Constrained Optimal Control for Linear Systems 14.
3.3 Dynamic Programming and the Backward Recursion 14.4 Exercises 14.5 Bibliographical Notes and Further Reading 15 Model Predictive Control 15.1 The Basic MPC Formulation 15.2 MPC Closed-Loop Analysis 15.2.1 Performance Estimates 15.
2.2 Closed-Loop Stability Properties 15.2.3 Viability and Recursive Feasibility 15.2.4 Hard and Soft Constraints 15.3 Model Predictive Control Schemes 15.3.
1 Time-Varying Systems and Reference Tracking 15.3.2 Linear MPC versus Nonlinear MPC 15.3.3 MPC without Terminal Costs and Constraints 15.3.4 Explicit MPC 15.3.
5 Economic MPC 15.3.6 Tube-Based MPC 15.4 Implementation Aspects of MPC 15.4.1 Warm-Start and Suboptimal MPC 15.4.2 Formulation of the Optimization Problem 15.
5 Exercises 15.6 Bibliographical Notes and Further Reading III Observer Design and Estimation 16 Observer Design for Linear Systems 16.1 Luenberger Observers 16.2 Minimum Energy Estimator (Continuous Time Setting) 16.3 The Discrete Time Kalman Filter 16.3.1 Least Squares and Minimum Variance Solution 16.3.
2 A Prediction-Correction Formulation 16.3.3 The Steady-State Kalman Filter 16.3.4 A Hybrid Time Kalman Filter 16.4 Exercises 16.5 Bibliographical Notes and Further Reading 17 Extended and Unscented Kalman Filter and Moving Horizon Estimation 17.1 Extended Kalman Filter (Continuous Time) 17.
2 Extended Kalman Filter (Discrete Time) 17.3 Unscented Kalman Filter (Discrete Time) 17.3.1 Unscented Transformation 17.3.2 Unscented Kalman Filter 17.4 Moving Horizon Estimation.