Preface	6
	Contents	10
	1 Convex Sets and Convex Functions	13
	1.1 Normed Spaces and Inner Product Spaces	13
	1.1.1 Sets and Mappings	13
	1.1.2 Normed Spaces	15
	1.1.3 Elementary Topology	19
	1.1.4 Limitation Theorems	21
	1.1.5 Inner Product Spaces	24
	1.2 Convex Sets	26
	1.2.1 Convex Sets and Their Properties	27
	1.2.2 Construction of Convex Sets	29
	1.2.3 Separation Theorems	35
	1.3 Convex Functions	40
	1.3.1 Convex Functions and Their Elementary Properties	40
	1.3.2 Examples of Convex Functions	43
	1.3.3 Derivative of Convex Functions	45
	1.4 Semi-continuous Functions	53
	1.4.1 Semi-continuous Functions and Their ElementaryProperties	53
	1.4.2 Examples of Semi-continuous Functions	57
	References	63
	2 Set-Valued Mappings and Differential Inclusions	64
	2.1 Set-Valued Mappings	64
	2.1.1 Definition of the Set-Valued Mappings	64
	2.1.2 Continuities of Set-Valued Mappings	66
	2.1.3 Tangent Cones and Normal Cones	73
	2.1.4 Derivative of Set-Valued Mappings	78
	2.2 Selection of Set-Valued Mappings	83
	2.2.1 The Minimal Selection	84
	2.2.2 Michael Selection Theorem	87
	2.2.3 Lipschitzian Approximation	91
	2.2.4 Theorems for Fixed Points	98
	2.3 Differential Inclusions and Existence Theorems	100
	2.3.1 Differential Equations and Differential Inclusions	100
	2.3.2 Why Do We Propose Differential Inclusions?	102
	2.3.3 Existence Theorems of Solution of Differential Inclusions	108
	2.3.4 The Existence of Solutions of Time-delayed Differential Inclusions	117
	2.4 Qualitative Analysis for Differential Inclusions	119
	2.4.1 Qualitative Analysis for Lipschitzian DifferentialInclusions	119
	2.4.2 Qualitative Analysis for Upper Semi-continuous Differential Inclusions	123
	2.4.3 Convexification of Differential Inclusions and Relaxed Theorem	129
	2.5 Stability of Differential Inclusions	135
	2.5.1 Dini Derivatives	135
	2.5.2 Definitions of Stability of Differential Inclusions	139
	2.5.3 Lyapunov-like Criteria for Stability of DifferentialInclusions	142
	2.6 Monotonous Differential Inclusions	151
	2.6.1 Monotonous Set-valued Mappings and Their Properties	152
	2.6.2 Minty Theorem	154
	2.6.3 Yosida Approximation	159
	2.6.4 Maximally Monotonous Differential Inclusions	163
	References	167
	3 Convex Processes	168
	3.1 Convex Processes in Linear Normed Spaces	168
	3.1.1 Convex Processes and Their Adjoint Processes	169
	3.1.2 The Norm of Convex Processes	174
	3.1.3 Fundamental Properties of Convex Processes	175
	3.2 Convex Processes in Spaces with Finite Dimensions	179
	3.2.1 Adjoint Processes in n-Dimensional Space	179
	3.2.2 Structure of Convex Processes	184
	3.3 Controllability of Convex Processes	196
	3.3.1 T-Controllability	196
	3.3.2 Controllability	203
	3.4 Stability of Convex Process Differential Inclusions	206
	3.4.1 Stability of Convex Processes	207
	3.4.2 Construction of Lyapunov Functions	214
	Reference	219
	4 Linear Polytope Control Systems	220
	4.1 Polytope Systems	220
	4.1.1 Linear Control Systems and Matrix Inequalities	220
	4.1.2 Linear Polytope Systems	225
	4.2 Convex Hull Lyapunov Functions	229
	4.2.1 Convex Hull Quadratic Lyapunov Functions	229
	4.2.2 Layer Sets for the Convex Hull Quadratic Function	232
	4.3 Control of Linear Polytope Systems	243
	4.3.1 Feedback Stabilizability for Linear Polytope Systems	244
	4.3.2 Feedback Stabilization for Linear Polytope Systems with Time-delay	250
	4.3.3 Disturbance Rejection for Linear Polytope Systems	253
	4.4 Saturated Control for Linear Control Systems	260
	4.4.1 Saturated Control Described by Set-Valued Mappings	260
	4.4.2 Stabilization by the Saturated Control	262
	4.4.3 Disturbance Rejection by the Saturated Control	267
	References	273
	5 Luré Differential Inclusion Systems	274
	5.1 Luré Systems	274
	5.1.1 Luré Systems and Absolute Stability	274
	5.1.2 Positive Realness and the Positive Realness Lemma	277
	5.1.3 Criterion for Absolute Stability	281
	5.2 Stabilization of Luré Differential Inclusion Systems	283
	5.2.1 An Example of the Luré Differential Inclusion System	284
	5.2.2 Stabilization of Luré Differential Inclusion Systems	286
	5.2.3 Zeroes and Relative Degree of Control Systems	287
	5.2.3.1 The Zeroes of System	287
	5.2.3.2 Relative Degree of System	288
	5.2.3.3 Hurwitz Vectors	291
	5.2.4 Feedback Positive Realness	292
	5.2.5 Feedback Stabilization – Single-Variable Systems	297
	5.2.6 Feedback Stabilization – Multivariable Systems	299
	5.3 Luenberger Observers and Separated Design	301
	5.3.1 Well-Posedness	302
	5.3.2 The Luenberger State Observer	304
	5.3.3 State Feedback Based on Observer	309
	5.3.4 Reduce-Order Luenberger Observer	311
	5.4 Linear Observers of Luré Differential Inclusion Systems	315
	5.4.1 Single-Variable Systems	316
	5.4.2 Multivariable Systems	323
	5.5 Adaptive Luenberger Observers	325
	5.5.1 Adaptive Luenberger Observers	326
	5.5.2 Reduced-Order Adaptive Observers	330
	5.5.3 An Example of Adaptive Observer	332
	5.6 Adaptive Linear Observers	335
	5.6.1 Persistent Excitation	336
	5.6.2 Linear Adaptive Observers	343
	References	350
	Index	351