Frequency-Domain Analysis and Design of Distributed Control Systems -- Contents -- Preface -- Glossary of Symbols -- 1 Introduction -- 1.1 Network-Based Distributed Control System -- 1.2 Graph Theory and Interconnection Topology -- 1.2.1 Basic Definitions -- 1.2.2 Graph Operations -- 1.2.3 Algebraic Graph Theory -- 1.3 Distributed Control Systems -- 1.3.1 End-to-End Congestion Control Systems -- 1.3.2 Consensus-Based Formation Control -- 1.4 Notes and References -- 1.4.1 Graph Theory and Distributed Control Systems -- 1.4.2 Delay in Control and Control by Delay -- References -- 2 Symmetry, Stability and Scalability -- 2.1 System Model -- 2.1.1 Graph-Based Model of Distributed Control Systems -- 2.1.2 Bipartite Distributed Control Systems -- 2.2 Symmetry in the Frequency Domain -- 2.2.1 Symmetric Systems -- 2.2.2 Symmetry of Bipartite Systems -- 2.3 Stability of Multivariable Systems -- 2.3.1 Poles and Stability -- 2.3.2 Zeros and Pole-Zero Cancelation -- 2.4 Frequency-Domain Criteria of Stability -- 2.4.1 Loop Transformation and Multiplier -- 2.4.2 Multivariable Nyquist Stability Criterion -- 2.4.3 Spectral Radius Theorem and Small-Gain Theorem -- 2.4.4 Positive Realness Theorem -- 2.5 Scalable Stability Criteria -- 2.5.1 Estimation of Spectrum of Complex Matrices -- 2.5.2 Scalable Stability Criteria for Asymmetric Systems -- 2.5.3 Scalable Stability Criteria for Symmetric Systems -- 2.5.4 Robust Stability in Deformity of Symmetry -- 2.6 Notes and References -- References -- 3 Scalability in the Frequency Domain -- 3.1 How the Scalability Condition is Related with Frequency Responses -- 3.2 Clockwise Property of Parameterized Curves -- 3.3 Scalability of First-Order Systems -- 3.3.1 Continuous-Time System -- 3.3.2 Discrete-Time System -- 3.4 Scalability of Second-Order Systems -- 3.4.1 System of Type I -- 3.4.2 System of Type II.

3.5 Frequency-Sweeping Condition -- 3.5.1 Stable Quasi-Polynomials -- 3.5.2 Frequency-Sweeping Test -- 3.6 Notes and References -- References -- 4 Congestion Control: Model and Algorithms -- 4.1 An Introduction to Congestion Control -- 4.1.1 Congestion Collapse -- 4.1.2 Efficiency and Fairness -- 4.1.3 Optimization-Based Resource Allocation -- 4.2 Distributed Congestion Control Algorithms -- 4.2.1 Penalty Function Approach and Primal Algorithm -- 4.2.2 Dual Approach and Dual Algorithm -- 4.2.3 Primal-Dual Algorithm -- 4.2.4 REM: A Second-Order Dual Algorithm -- 4.3 A General Model of Congestion Control Systems -- 4.3.1 Framework of End-to-End Congestion Control under Diverse Round-Trip Delays -- 4.3.2 General Primal-Dual Algorithm -- 4.3.3 Frequency-Domain Symmetry of Congestion Control Systems -- 4.4 Notes and References -- References -- 5 Congestion Control: Stability and Scalability -- 5.1 Stability of the Primal Algorithm -- 5.1.1 Johari-Tan Conjecture -- 5.1.2 Scalable Stability Criterion for Discrete-Time Systems -- 5.1.3 Scalable Stability Criterion for Continuous-Time Systems -- 5.2 Stability of REM -- 5.2.1 Scalable Stability Criteria -- 5.2.2 Dual Algorithm: the First-Order Limit Form of REM -- 5.2.3 Design of Parameters of REM -- 5.3 Stability of the Primal-Dual Algorithm -- 5.3.1 Scalable Stability Criteria -- 5.3.2 Proof of the Stability Criteria -- 5.4 Time-Delayed Feedback Control -- 5.4.1 Time-Delayed State as a Reference -- 5.4.2 TDFC for Stabilization of an Unknown Equilibrium -- 5.4.3 Limitation of TDFC in Stabilization -- 5.5 Stabilization of Congestion Control Systems by Time-Delayed Feedback Control -- 5.5.1 Introduction of TDFC into Distributed Congestion Control Systems -- 5.5.2 Stabilizability under TDFC -- 5.5.3 Design of TDFC with Commensurate Self-Delays -- 5.6 Notes and References.

5.6.1 Stability of Congestion Control with Propagation Delays -- 5.6.2 Time-Delayed Feedback Control -- References -- 6 Consensus in Homogeneous Multi-Agent Systems -- 6.1 Introduction to Consensus Problem -- 6.1.1 Integrator Agent System -- 6.1.2 Existence of Consensus Solution -- 6.1.3 Consensus as a Stability Problem -- 6.1.4 Discrete-Time Systems -- 6.1.5 Consentability -- 6.2 Second-Order Agent System -- 6.2.1 Consensus and Stability -- 6.2.2 Consensus and Consentability Condition -- 6.2.3 Periodic Consensus Solutions -- 6.2.4 Simulation Study -- 6.3 High-Order Agent System -- 6.3.1 System Model -- 6.3.2 Consensus Condition -- 6.3.3 Consentability -- 6.4 Notes and References -- References -- 7 Consensus in Heterogeneous Multi-Agent Systems -- 7.1 Integrator Agent System with Diverse Input and Communication Delays -- 7.1.1 Consensus in Discrete-Time Systems -- 7.1.2 Consensus under Diverse Input Delays -- 7.1.3 Consensus under Diverse Communication Delays and Input Delays -- 7.1.4 Continuous-Time System -- 7.1.5 Simulation Study -- 7.2 Double Integrator System with Diverse Input Delays and Interconnection Uncertainties -- 7.2.1 Leader-Following Consensus Algorithm -- 7.2.2 Consensus Condition under Symmetric Coupling Weights -- 7.2.3 Robust Consensus under Asymmetric Perturbations -- 7.2.4 Simulation Study -- 7.3 High-Order Consensus in High-Order Systems -- 7.3.1 System Model -- 7.3.2 Consensus Condition -- 7.3.3 Existence of High-Order Consensus Solutions -- 7.3.4 Constant Consensus -- 7.3.5 Consensus in Ideal Networks -- 7.4 Integrator-Chain Systems with Diverse Communication Delays -- 7.4.1 Matching Condition for Self-Delay -- 7.4.2 Adaptive Adjustment of Self-Delay -- 7.4.3 Simulation Study -- 7.5 Notes and References -- References -- Index.