Chapter
1.3.3 Stability of Linear Systems
1.3.4 Finite-Time Stability of Continuous System
1.3.5 Stability of Discontinuous Systems
1.3.6 Proof of Theorem 1.3.11
1.4 Remarks and Bibliographical Notes
Chapter 2 The Tracking Differentiator (TD)
2.1 Linear Tracking Differentiator
2.2 Nonlinear Tracking Differentiator
2.2.1 Second-Order Nonlinear Tracking Differentiator
2.2.2 High-Order Nonlinear Tracking Differentiator
2.3 Finite-Time Stable System-Based Tracking Differentiator
2.3.1 Convergence of Finite-Time Stable System-Based TD
2.3.2 A Second-Order Finite-Time Stable Tracking Differentiator
2.4 Illustrative Examples and Applications
2.4.1 Comparison of Three Differentiators
2.4.2 Applications to Frequency Online Estimation
2.4.3 Application to the Boundary Stabilization of Wave Equation
2.5 Summary and Open Problems
2.6 Remarks and Bibliographical Notes
Chapter 3 Extended State Observer
3.1 Linear Extended State Observer for SISO Systems
3.2 Nonlinear Extended State Observer for SISO Systems
3.2.1 Nonlinear ESO for SISO Systems
3.3 The ESO for SISO Systems with Time-Varying Gain
3.4 The ESO for MIMO Systems with Uncertainty
3.4.1 ESO for Systems with Total Disturbance
3.4.2 ESO for Systems with External Disturbance Only
3.4.3 Examples and Numerical Simulations
3.5 Summary and Open Problems
3.6 Remarks and Bibliographical Notes
Chapter 4 The Active Disturbance Rejection Control
4.1 Linear ADRC for SISO Systems
4.1.1 Global Convergence of Linear ADRC for SISO Systems
4.1.2 Global Convergence for Systems with External Disturbance Only
4.1.3 Semi-Global Convergence of LADRC
4.1.4 Numerical Simulations
4.2 Nonlinear ADRC for SISO Systems
4.2.1 Global ADRC for SISO Systems with Total Disturbance
4.2.2 Global ADRC for SISO System with External Disturbance Only
4.2.3 Semi-global ADRC for SISO System with Vast Uncertainty
4.2.4 Examples and Numerical Simulations
4.3 ADRC with Time-Varying Tuning Parameter
4.4 Nonlinear ADRC for MIMO Systems with Vast Uncertainty
4.4.1 Semi-Global ADRC for MIMO Systems with Uncertainty
4.4.2 Global ADRC for MIMO Systems with Uncertainty
4.4.3 Global ADRC for MIMO Systems with External Disturbance Only
4.4.4 Numerical Simulations
4.6 HGC and SMC Versus ADRC
4.7 Applications to PMSMs
4.8 Application to Wave Equation with Uncertainty
4.8.2 Proof of Theorem 4.8.1
4.9 Summary and Open Problems
4.10 Remarks and Bibliographical Notes
Chapter 5 ADRC for Lower Triangular Nonlinear Systems
5.1 ESO for Lower Triangular Systems
5.1.1 Constant High-Gain ESO
5.1.2 Time-Varying Gain ESO
5.1.3 Numerical Simulation
5.2 Stabilization of Lower Triangular Systems by ADRC
5.2.1 ADRC with Constant Gain ESO
5.2.2 ADRC with Time-Varying Gain ESO
5.3 Numerical Simulations
5.4 Summary and Open Problems
5.5 Remarks and Bibliographical Notes
Active Disturbance Rejection Control for Nonlinear Systems
：An Introduction
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