Consensus Over Switching Network Topology: Characterizing System Parameters and Joint Connectivity

Preface
Contents
1 Introduction
	1.1 Background
	1.2 Outline and Overview of the Chapters
	1.3 Preliminary
		1.3.1 Digraph and Matrix
		1.3.2 Dynamically Changing Digraph
		1.3.3 Nonnegative Matrix and M-Matrix Theory
		1.3.4 Kronecker Product
		1.3.5 Notations
2 Consensus of Double-Integrators over Switching Network Topology
	2.1 Continuous-Time Systems with Piecewise Fixed Network Topology
		2.1.1 Agent Model Without/with Communication Delay
		2.1.2 Stationary Consensus without Communication Delay
		2.1.3 Stationary Consensus with Communication Delay
		2.1.4 Numerical Examples
		2.1.5 Conclusion
		2.1.6 Appendix
	2.2 Sampled-Data Systems with Piecewise Continuous Network Topology
		2.2.1 Sampled-Data Agent Model with Nonuniform and Time-Varying Communication Delays
		2.2.2 Graph Augmentation and Joint Connectivity
		2.2.3 Consensus via Product of Stochastic Matrices
		2.2.4 Numerical Examples
		2.2.5 Conclusion
		2.2.6 Appendix
	2.3 Asynchronous Update Systems with Piecewise Continuous Network Topology
		2.3.1 Asynchronous Update Agent Model
		2.3.2 Consensus for Asynchronous Update
		2.3.3 Consensus Analysis via Augmented Synchronous Update
		2.3.4 Numerical Examples
		2.3.5 Conclusion
3 Generic Linear Systems over Undirected Network: Controllability and Connectivity
	3.1 Piecewise Continuous and Balanced Network Topology
		3.1.1 Network Configuration
		3.1.2 Weakly Connected Network Topology (WCNT)
		3.1.3 WCNT with Communication Constraints
		3.1.4 Repeatedly Jointly WCNT
		3.1.5 Numerical Examples
		3.1.6 Conclusion
		3.1.7 Appendix
	3.2 Piecewise Fixed Network Topology: Necessary and Sufficient Conditions
		3.2.1 Problem Reformulation and Preliminary Results
		3.2.2 A Subspace Method for Consensus Analysis
		3.2.3 Extension to Unstable System Dynamics
		3.2.4 Conclusion
		3.2.5 Appendix: Technical Analysis
	3.3 Continuously Time-varying Network Topology via Uniform Complete Observability Theory
		3.3.1 Agent Model and Network Configuration
		3.3.2 Uniform Complete Observability
		3.3.3 A Compact Set of Matrix-Valued Functions  and Exponential Consensus
		3.3.4 Further Discussions and Conclusion
		3.3.5 Appendix: Proof of Lemma 3.56
4 Generic Linear Systems over Directed Switching Network Topology
	4.1 Discrete-Time Systems with Invertible Input Matrix
		4.1.1 Agent Model and Network Configuration
		4.1.2 Theoretical Results and Convergence Analysis
		4.1.3 Further Analysis and Extensions
		4.1.4 Numerical Examples
		4.1.5 Conclusion
	4.2 Continuous-Time Systems with Invertible Input Matrix
		4.2.1 Agent Model and Network Configuration
		4.2.2 Theoretical Results and Convergence Analysis
		4.2.3 Numerical Examples
		4.2.4 Conclusion
	4.3 Non-invertible Input Matrix: an Algebraic and Geometric Perspective
		4.3.1 System Model and Preliminary Results
		4.3.2 Convergence Analysis over Any Subinterval Without Connectivity Requirement
		4.3.3 Synchronization Under Joint Connectivity Condition
		4.3.4 Numerical Examples
		4.3.5 Proof of the Main Results
		4.3.6 Conclusion
		4.3.7 Appendix
5 Extensions to Containment Control
	5.1 Collective Behavior of Generic Linear Agents …
		5.1.1 Continuous-Time Setting
		5.1.2 Discrete-Time Counterpart
		5.1.3 Application to Consensus and Containment Control
		5.1.4 Numerical Examples
		5.1.5 Conclusion
	5.2 Output Containment Control with Fixed and Switching Topologies
		5.2.1 Agent Model and Problem Definition
		5.2.2 A Necessary Condition from Internal Model Principle
		5.2.3 Output Containment over Fixed Network Topology
		5.2.4 Output Containment over Dynamic Network
		5.2.5 Optimal Model-Free Output Containment
		5.2.6 Numerical Examples
		5.2.7 Conclusion
	5.3 Containment Control: a Novel State Transition Matrix Perspective
		5.3.1 Agent Model and Problem Statement
		5.3.2 The Consensus Pattern in Multi-Leader MASs
		5.3.3 Containment of Positive Linear Systems
		5.3.4 Second-Order Agents
		5.3.5 Conclusion
References