Preface ...................................................... xiii
Chapter 1. Introduction ......................................... 1
1.1 Large-Scale Interconnected Dynamical Systems ............... 1
1.2 A Brief Outline of the Monograph ........................... 5
Chapter 2. Stability Theory via Vector Lyapunov Functions ....... 9
2.1 Introduction ............................................... 9
2.2 Notation and Definitions ................................... 9
2.3 Quasi-Monotone and Essentially Nonnegative Vector Fields .. 10
2.4 Generalized Differential Inequalities ..................... 14
2.5 Stability Theory via Vector Lyapunov Functions ............ 18
2.6 Discrete-Time Stability Theory via Vector Lyapunov
Functions ................................................. 34
Chapter 3. Large-Scale Continuous-Time Interconnected
Dynamical Systems .............................................. 45
3.1 Introduction .............................................. 45
3.2 Vector Dissipativity Theory for Large-Scale Nonlinear
Dynamical Systems ......................................... 46
3.3 Extended Kalman-Yakubovich-Popov Conditions for Large-
Scale Nonlinear Dynamical Systems ......................... 61
3.4 Specialization to Large-Scale Linear Dynamical Systems .... 68
3.5 Stability of Feedback Interconnections of Large-Scale
Non-linear Dynamical Systems .............................. 71
Chapter 4. Thermodynamic Modeling of Large-Scale
Interconnected Systems ......................................... 75
4.1 Introduction .............................................. 75
4.2 Conservation of Energy and the First Law of
Thermodynamics ............................................ 75
4.3 Nonconservation of Entropy and the Second Law of
Thermodynamics ............................................ 79
4.4 Semistability and Large-Scale Systems ..................... 82
4.5 Energy Equipartition ...................................... 86
4.6 Entropy Increase and the Second Law of Thermodynamics ..... 88
4.7 Thermodynamic Models with Linear Energy Exchange .......... 90
Chapter 5. Control of Large-Scale Dynamical Systems via Vector
Lyapunov Functions ............................................. 93
5.1 Introduction .............................................. 93
5.2 Control Vector Lyapunov Functions ......................... 94
5.3 Stability Margins, Inverse Optimality, and Vector
Dissipativity ............................................. 99
5.4 Decentralized Control for Large-Scale Nonlinear
Dynamical Systems ........................................ 102
Chapter 6. Finite-Time Stabilization of Large-Scale Systems
via Control Vector Lyapunov Functions ......................... 107
6.1 Introduction ............................................. 107
6.2 Finite-Time Stability via Vector Lyapunov Functions ...... 108
6.3 Finite-Time Stabilization of Large-Scale Dynamical
Systems .................................................. 114
6.4 Finite-Time Stabilization for Large-Scale Homogeneous
Systems .................................................. 119
6.5 Decentralized Control for Finite-Time Stabilization of
Large-Scale Systems ...................................... 121
Chapter 7. Coordination Control for Multiagent
Interconnected Systems ........................................ 127
7.1 Introduction ............................................. 127
7.2 Stability and Stabilization of Time-Varying Sets ......... 129
7.3 Control Design for Multivehicle Coordinated Motion ....... 135
7.4 Stability and Stabilization of Time-Invariant Sets ....... 141
7.5 Control Design for Static Formations ..................... 144
7.6 Obstacle Avoidance in Multivehicle Coordination .......... 145
Chapter 8. Large-Scale Discrete-Time Interconnected Dynamical
Systems ....................................................... 153
8.1 Introduction ............................................. 153
8.2 Vector Dissipativity Theory for Discrete-Time Large-
Scale Nonlinear Dynamical Systems ........................ 154
8.3 Extended Kalman-Yakubovich-Popov Conditions for
Discrete-Time Large-Scale Nonlinear Dynamical Systems .... 168
8.4 Specialization to Discrete-Time Large-Scale Linear
Dynamical Systems ........................................ 173
8.5 Stability of Feedback Interconnections of Discrete-Time
Large-Scale Nonlinear Dynamical Systems .................. 177
Chapter 9. Thermodynamic Modeling for Discrete-Time Large-
Scale Dynamical Systems ....................................... 181
9.1 Introduction ............................................. 181
9.2 Conservation of Energy and the First Law of
Thermodynamics ........................................... 182
9.3 Nonconservation of Entropy and the Second Law of
Thermodynamics ........................................... 187
9.4 Nonconservation of Ectropy ............................... 189
9.5 Semistability of Discrete-Time Thermodynamic Models ...... 191
9.6 Entropy Increase and the Second Law of Thermodynamics .... 198
9.7 Thermodynamic Models with Linear Energy Exchange ......... 200
Chapter 10. Large-Scale Impulsive Dynamical Systems ........... 211
10.1 Introduction ............................................. 211
10.2 Stability of Impulsive Systems via Vector Lyapunov
Functions ................................................ 213
10.3 Vector Dissipativity Theory for Large-Scale Impulsive
Dynamical Systems ........................................ 224
10.4 Extended Kalman-Yakubovich-Popov Conditions for
Large-Scale Impulsive Dynamical Systems .................. 249
10.5 Specialization to Large-Scale Linear Impulsive
Dynamical Systems ........................................ 259
10.6 Stability of Feedback Interconnections of Large-Scale
Impulsive Dynamical Systems .............................. 264
Chapter 11. Control Vector Lyapunov Functions for Large-
Scale Impulsive Systems ....................................... 271
11.1 Introduction ............................................. 271
11.2 Control Vector Lyapunov Functions for Impulsive
Systems .................................................. 272
11.3 Stability Margins and Inverse Optimality ................. 279
11.4 Decentralized Control for Large-Scale Impulsive
Dynamical Systems ........................................ 284
Chapter 12. Finite-Time Stabilization of Large-Scale
Impulsive Dynamical Systems ................................... 289
12.1 Introduction ............................................. 289
12.2 Finite-Time Stability of Impulsive Dynamical Systems ..... 289
12.3 Finite-Time Stabilization of Impulsive Dynamical
Systems .................................................. 297
12.4 Finite-Time Stabilizing Control for Large-Scale
Impulsive Dynamical Systems .............................. 300
Chapter 13. Hybrid Decentralized Maximum Entropy Control for
Large-Scale Systems ........................................... 305
13.1 Introduction ............................................. 305
13.2 Hybrid Decentralized Control and Large-Scale Impulsive
Dynamical Systems ........................................ 306
13.3 Hybrid Decentralized Control for Large-Scale Dynamical
Systems .................................................. 313
13.4 Interconnected Euler-Lagrange Dynamical Systems .......... 319
13.5 Hybrid Decentralized Control Design ...................... 323
13.6 Quasi-Thermodynamic Stabilization and Maximum Entropy
Control .................................................. 327
13.7 Hybrid Decentralized Control for Combustion Systems ...... 335
13.8 Experimental Verification of Hybrid Decentralized
Controller ............................................... 341
Chapter 14. Conclusion ........................................ 351
Bibliography .................................................. 353
Index ......................................................... 367
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