Preface	7
	Contents	10
	Symbols and Abbreviations	13
	1 Introduction	15
	1.1 Examples of Time-Delay Systems	15
	1.1.1 A Gyroscopic System	15
	1.1.2 A Classical Economic Model	16
	1.1.3 Communication Networks	18
	1.1.4 Biological Systems	20
	1.1.5 The Dujiangyan Irrigation Project: A Showcase of Early Mankind's Ingenuity	21
	1.2 Linear Time-Delay Systems	23
	1.2.1 Stability of Linear Time-Delay Systems	25
	1.2.2 Stabilization of Linear Time-Delay Systems	27
	1.3 Delays in Networked Control Systems	29
	1.4 Delays in Multi-agent Systems	31
	1.5 Summary	33
	2 Mathematical Background	34
	2.1 Signal and System Norms	34
	2.1.1 mathcalL2 and mathcalH2 Norms	35
	2.1.2 mathcalLp-Induced System Norms	37
	2.2 Small-Gain Theorems	38
	2.2.1 mathcalL2 Small-Gain Theorem	39
	2.2.2 mathcalLinfty Small-Gain Theorem	40
	2.2.3 Mean-Square Small-Gain Theorem	41
	2.3 mathcalHinfty and mathcalH2 Optimal Control	43
	2.3.1 Youla–Kuera Parameterization	44
	2.3.2 Inner–Outer Factorization	46
	2.4 Robust Stability Margin Problems	49
	2.4.1 System Poles and Zeros	49
	2.4.2 Analytic Function Interpolation	51
	2.4.3 Gain and Phase Margin Problems	52
	2.5 LMI and GEVP	54
	2.6 Summary	55
	3 Small-Gain Stability Conditions	56
	3.1 Introduction	56
	3.2 Uncertainty Modeling and Model Transformation	57
	3.3 mathcalL2-Stability Conditions	61
	3.3.1 Range-Independent Conditions	61
	3.3.2 Range-Dependent Conditions	63
	3.3.3 Extension to Noncentric Delay Intervals	69
	3.3.4 Extension to Transformed Nominal Systems	72
	3.4 mathcalLinfty-Stability Conditions	74
	3.4.1 Delay-Independent Conditions	75
	3.4.2 Delay-Dependent Conditions	79
	3.5 Summary	82
	4 Delay Margin	84
	4.1 Introduction	84
	4.2 Upper Bounds on the Delay Margin	86
	4.3 Lower Bounds on the Delay Margin	92
	4.4 Summary	105
	5 Stabilization of Linear Systems with Time-Varying Delays	107
	5.1 Introduction	107
	5.2 Rate-Independent Bound	109
	5.3 Rate-Dependent Conditions	110
	5.4 Summary	119
	6 Delay Margin Achievable by PID Controllers	120
	6.1 Introduction	120
	6.2 First-Order Unstable Systems	123
	6.3 Second-Order Unstable Plants	127
	6.3.1 Real Poles	127
	6.3.2 Complex Conjugate Poles	134
	6.3.3 Oscillatory Poles	137
	6.4 Second-Order Examples	139
	6.5 Effect of Nonminimum Phase Zeros	143
	6.6 Unstable Plants with Time-Varying Delay	146
	6.7 Summary	154
	7 Delay Radius of MIMO Delay Systems	0
	7.1 Introduction	155
	7.2 Region of Stability	157
	7.3 Uniform Delays	164
	7.4 Region of Instability	165
	7.5 Summary	175
	8 Stabilization of Networked Delay Systems	176
	8.1 Introduction	176
	8.2 Mean-Square Stabilizability	178
	8.3 SISO Systems	179
	8.4 MIMO Systems	186
	8.5 Summary	195
	9 Consensus of Multi-agent Systems Under Delay	196
	9.1 Introduction	196
	9.2 Consensus over Undirected Graph	198
	9.3 Consensus over Directed Graph	211
	9.4 Summary	217
	Appendix References	218
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