Part I Introduction and Preliminaries 1 Introduction 1.1 Event-Triggered Control Challenges for Nonlinear Systems 1.2 An Overview of This Book 2 Basic Stability and Small-Gain Tools for System Synthesis 2.1 Lyapunov Stability 2.2 Input-to-State Stability 2.2.1 Definition 2.2.2 ISS-Lyapunov Functions 2.3 Nonlinear Small-Gain Theorem 2.3.1 Trajectory-Based Small-Gain Theorem 2.3.2 Lyapunov-Based Small-Gain Theorem 2.4 Nonlinear Cyclic-Small-Gain Theorem 2.4.1 Continuous-Time Systems 2.4.2 Equivalence Between Cyclic-Small-Gain and Gains Less Than the Identity 2.5 Notes Part II Robust Event Triggers 3 A Small-Gain Paradigm for Event-Triggered Control 3.1 Problem Formulation 3.2 Lyapunov-Based Small-Gain Design of Event Triggers 3.3 Trajectory-Based Small-Gain Design of Event Triggers 3.4 Event/Self-Triggered Control in the Presence of External Disturb ances 3.4.1 Event Triggers with Positive Offsets 3.4.2 Self-Triggered Control 3.4.3 Trajectory-Based Formulation 3.5 Input-to-State Stabilization of Discrete-Time Nonlinear Systems 3.5.1 Problem Formulation 3.5.2 Event-Triggered Robust Stabilization 3.6 Notes 4 Dynamic Event Triggers 4.1 Dynamic Event Triggers with Partial-State Feedback 4.1.1 Problem Formulation 4.1.2 Design of a Dynamic Event Trigger 4.1.3 An Extension 4.2 An Application to Decentralized Event-Triggered Control 4.2.1 Problem Formulation 4.2.2 Design of Decentralized Event-Triggers 4.2.3 An Example: Decentralized Event-Triggered Control of a Class of First-Order Nonlinear Systems 4.2.4 The Linear Case 4.3 Notes 5 Event-Triggered Input-to-State Stabilization Robust Event-Triggered Control of Nonlinear Systems under a 5.1 Global Sector-Bound Condition 5.2 Robust Event-Triggered Control of Nonlinear Systems without a Global Sector-Bound Condition 5.3 Robustness Analysis in the Presence of
Dynamic Uncertainties 5.3.1 Event Trigger Design 5.3.2 Small-Gain Synthesis: ISS of the Closed-Loop Event-Triggered System 5.3.3 A Special Case for Systems Under a Global Sector-Bound Condition 5.4 An Extension to Systems Subject to Both Dynamic Uncertainties and External Disturbances 5.5 Notes Part III Constructive Designs for Event-Triggered Control 6 Event-Triggered Control of Nonlinear Uncertain Systems in the Lower-Tri angular Form 6.1 Event-Triggered State-Feedback Control 6.1.1 Problem Formulation 6.1.2 Controller Design 6.1.3 Small-Gain Synthesis 6.2 Event-Triggered Control of Nonlinear Time-Delay Systems 6.2.1 Problem Formulation 6.2.2 Constructive Control Design with Set-Valued Maps 6.2.3 Main Result of Event-Triggered Stabilization 6.2.4 Extension to Systems with Distributed Time-Delays 6.3 Event-Triggered Output-Feedback Control 6.3.1 Problem Formulation 6.3.2 Observer-Based Output-Feedback Controller 6.3.3 ISS Property of the Subsystems 6.3.4 Event-Triggered Output-Feedback Control 6.4 Notes 7 Event-Triggered Control of Nonholonomic Svstems 7.1 Event-Triggered State Feedback Control of Uncertain Nonholo nomic Systems 7.1.1 Problem Formulation 7.1.2 Event-Triggered State-Feedback Controller 7.1.3 Main Result 7.1.4 A Brief Discussion on x (t)=0 7.2 Event-Triggered Output Feedback Control of Uncertain Nonholo nomic Systems 7.2.1 Problem Formulation 7.2.2 Event-Triggered Output-Feedback Controller 7.2.3 Main Result 7.3 Notes Appendix A Notions A.1 Lipschitz Continuity A.2 Comparison Functions A.3 Related Notions in Graph Theory Appendix B Technical Lemmas Appendix C Gain Assignment Appendix D Proofs D.1 Proof of Theorem 2.6 D.2 Proof of Theorem 2.8 D.3 More Remarks about Example 4.2
D.4 Proof of Lemma 4.1 D.5 Proof of Lemma 4.2 D.6 Proof of Lemma 6.1 D.7 Proof of Proposition 6.1 D.8 Proof of Proposition 6.2 D.9 Proof of Proposition 7.2 D.10 Proof of Proposition 7.3 D.11 Proof of Proposition 7.4 D.12 Proof of Proposition 7.5 D.13 Proof of Proposition 7.9 References Index
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