Chapter
2.15 Notes and References
Chapter Three: Stability Theory for Nonlinear Dynamical Systems
3.2 Lyapunov Stability Theory
3.3 Invariant Set Stability Theorems
3.4 Construction of Lyapunov Functions
3.5 Converse Lyapunov Theorems
3.6 Lyapunov Instability Theorems
3.7 Stability of Linear Systems and Lyapunov’s Linearization Method
Chapter Four: Advanced Stability Theory
4.2 Partial Stability of Nonlinear Dynamical Systems
4.3 Stability Theory for Nonlinear Time-Varying Systems
4.4 Lagrange Stability, Boundedness, and Ultimate Boundedness
4.5 Input-to-State Stability
4.6 Finite-Time Stability of Nonlinear Dynamical Systems
4.7 Semistability of Nonlinear Dynamical Systems
4.8 Generalized Lyapunov Theorems
4.9 Lyapunov and Asymptotic Stability of Sets
4.10 Poincaré Maps and Stability of Periodic Orbits
4.11 Stability Theory via Vector Lyapunov Functions
4.13 Notes and References
Chapter Five: Dissipativity Theory for Nonlinear Dynamical Systems
5.2 Dissipative and Exponentially Dissipative Dynamical Systems
5.3 Lagrangian and Hamiltonian Dynamical Systems
5.4 Extended Kalman-Yakubovich-Popov Conditions for Nonlinear Dynamical Systems
5.5 Linearization of Dissipative Dynamical Systems
5.6 Positive Real and Bounded Real Dynamical Systems
5.7 Absolute Stability Theory
5.8 The Positivity Theorem and the Circle Criterion
5.11 Notes and References
Chapter Six: Stability and Optimality of Feedback Dynamical Systems
6.2 Feedback Interconnections of Dissipative Dynamical Systems
6.3 Energy-Based Feedback Control
6.4 Stability Margins for Nonlinear Feedback Regulators
6.5 Control Lyapunov Functions
6.6 Optimal Control and the Hamilton-Jacobi-Bellman Equation
6.7 Feedback Linearization, Zero Dynamics, and Minimum-Phase Systems
Chapter Seven: Input-Output Stability and Dissipativity
7.2 Input-Output Stability
7.3 The Small Gain Theorem
7.4 Input-Output Dissipativity Theory
7.5 Input-Output Operator Dissipativity Theory
7.6 Connections Between Input-Output Stability and Lyapunov Stability
7.7 Induced Convolution Operator Norms of Linear Dynamical Systems
7.8 Induced Convolution Operator Norms of Linear Dynamical Systems and … Stability
7.9 Finitely Computable Upper Bounds for |||G|||(∞,p),(1,r)
7.10 Upper Bounds for … Operator Norms
7.12 Notes and References
Chapter Eight: Optimal Nonlinear Feedback Control
8.2 Stability Analysis of Nonlinear Systems
8.3 Optimal Nonlinear Control
8.4 Inverse Optimal Control for Nonlinear Affine Systems
8.5 Gain, Sector, and Disk Margins of Nonlinear-Nonquadratic Optimal Regulators
8.6 Inverse Optimality of Nonlinear Regulators
8.7 Linear-Quadratic Optimal Regulators
8.8 Stability Margins, Meaningful Inverse Optimality, and Control Lyapunov Functions
8.10 Notes and References
Chapter Nine: Inverse Optimal Control and Integrator Backstepping
9.2 Cascade and Block Cascade Control Design
9.3 Optimal Integrator Backstepping Controllers
9.4 Optimal Linear Block Backstepping Controllers
9.5 Optimal Nonlinear Block Backstepping Controllers
9.6 Rotating Stall and Surge Control for Axial Compression Systems
9.7 Surge Control for Centrifugal Compressors
Chapter Ten: Disturbance Rejection Control for Nonlinear Dynamical Systems
10.2 Nonlinear Dissipative Dynamical Systems with Bounded Disturbances
10.3 Specialization to Dissipative Systems with Quadratic Supply Rates
10.4 A Riccati Equation Characterization for Mixed … Performance
10.5 Nonlinear-Nonquadratic Controllers for Systems with Bounded Disturbances
10.6 Optimal and Inverse Optimal Control for Affine Systems with … Disturbances
10.7 Stability Margins, Meaningful Inverse Optimality, and Nonexpansive Control Lyapunov Functions
10.8 Nonlinear Controllers with Multilinear and Polynomial Performance Criteria
10.10 Notes and References
Chapter Eleven: Robust Control for Nonlinear Uncertain Systems
11.2 Robust Stability Analysis of Nonlinear Uncertain Systems
11.3 A Dissipative Systems Perspective on Robust Stability
11.4 Robust Optimal Control for Nonlinear Uncertain Systems
11.5 Optimal and Inverse Optimal Robust Control for Nonlinear Uncertain Affine Systems
11.6 Nonlinear Guaranteed Cost Control
11.7 Stability Margins, Meaningful Inverse Optimality, and Robust Control Lyapunov Functions
11.8 Robust Nonlinear Controllers with Polynomial Performance Criteria
11.9 Robust Nonlinear Controllers with Multilinear Performance Criteria
11.11 Notes and References
Chapter Twelve: Structured Parametric Uncertainty and Parameter-Dependent Lyapunov Functions
12.2 Linear Uncertain Systems and the Structured Singular Value
12.3 Robust Stability Analysis of Nonlinear Uncertain Systems via Parameter-Dependent Lyapunov Functions
12.4 Robust Optimal Control for Nonlinear Systems via Parameter-Dependent Lyapunov Functions
12.5 Robust Control for Nonlinear Uncertain Affine Systems
12.6 Robust Nonlinear Controllers with Polynomial Performance Criteria
12.7 Robust Nonlinear Controllers with Multilinear Performance Criteria
12.9 Notes and References
Chapter Thirteen: Stability and Dissipativity Theory for Discrete-Time Nonlinear Dynamical Systems
13.2 Discrete-Time Lyapunov Stability Theory
13.3 Discrete-Time Invariant Set Stability Theorems
13.4 Converse Lyapunov Theorems for Discrete-Time Systems
13.5 Partial Stability of Discrete-Time Nonlinear Dynamical Systems
13.6 Stability Theory for Discrete-Time Nonlinear Time-Varying Systems
13.7 Lagrange Stability, Boundedness, and Ultimate Boundedness
13.8 Stability Theory via Vector Lyapunov Functions
13.9 Dissipative and Geometrically Dissipative Discrete-Time Dynamical Systems
13.10 Extended Kalman-Yakubovich-Popov Conditions for Discrete-Time Dynamical Systems
13.11 Linearization of Dissipative Dynamical Systems
13.12 Positive Real and Bounded Real Discrete-Time Dynamical Systems
13.13 Feedback Interconnections of Dissipative Dynamical Systems
13.14 Stability Margins of Discrete Regulators
13.15 Control Lyapunov Functions for Discrete-Time Systems
13.17 Notes and References
Chapter Fourteen: Discrete-Time Optimal Nonlinear Feedback Control
14.2 Optimal Control and the Bellman Equation
14.3 Stability Analysis of Discrete-Time Nonlinear Systems
14.4 Optimal Discrete-Time Nonlinear Control
14.5 Inverse Optimal Control for Nonlinear Affine Systems
14.6 Gain, Sector, and Disk Margins of Discrete-Time Optimal Regulators
14.7 Linear-Quadratic Optimal Regulators
14.8 Stability Margins, Meaningful Inverse Optimality, and Control Lyapunov Functions
14.9 Nonlinear Discrete-Time Dynamical Systems with Bounded Disturbances
14.10 Specialization to Dissipative Systems with Quadratic Supply Rates
14.11 A Riccati Equation Characterization for Mixed H2/ℓ1 Performance
14.12 Robust Stability Analysis of Nonlinear Uncertain Discrete-Time Systems
14.14 Notes and References
Nonlinear Dynamical Systems and Control
：A Lyapunov-Based Approach
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