Preface ........................................................ xv
Chapter 1. Introduction ......................................... 1
Chapter 2. Stability Theory for Nonnegative Dynamical Systems ... 7
2.1 Introduction ............................................... 7
2.2 Lyapunov Stability Theory for Nonnegative Dynamical
Systems .................................................... 7
2.3 Invariant Set Stability Theorems .......................... 16
2.4 Semistability of Nonnegative Dynamical Systems ............ 21
2.5 Stability Theory for Linear Nonnegative Dynamical
Systems ................................................... 30
2.6 Nonlinear Compartmental Dynamical Systems ................. 43
2.7 Compartmental Systems in Biology, Ecology, Epidemiology,
and Pharmacology .......................................... 49
2.8 Discrete-Time Lyapunov Stability Theory for Nonnegative
Dynamical Systems ......................................... 61
2.9 Discrete-Time Invariant Set Theorems and Semistability
Theorems .................................................. 64
2.10 Stability Theory for Discrete-Time Linear Nonnegative
Dynamical Systems ......................................... 69
2.11 Discrete-Time Nonlinear Compartmental Dynamical Systems ... 83
Chapter 3. Stability Theory for Nonnegative and Compartmental
Dynamical Systems with Time Delay ................... 89
3.1 Introduction .............................................. 89
3.2 Lyapunov Stability Theory for Time-Delay Nonnegative
Dynamical Systems ......................................... 90
3.3 Invariant Set Stability Theorems .......................... 93
3.4 Stability Theory for Continuous-Time Nonnegative
Dynamical Systems with Time Delay ......................... 97
3.5 Discrete-Time Lyapunov Stability Theory for Time-Delay
Nonnegative Dynamical Systems ............................ 103
3.6 Stability Theory for Discrete-Time Nonnegative
Dynamical Systems with Time Delay ........................ 106
Chapter 4. Nonoscillation and Monotonicity of Solutions of
Nonnegative Dynamical Systems ..................... 111
4.1 Introduction ............................................. 1ll
4.2 Nonoscillation and Monotonicity of Linear Nonnegative
Dynamical Systems ........................................ 112
4.3 Mammillary Systems ....................................... 119
4.4 Monotonicity of Nonlinear Nonnegative Dynamical
Systems .................................................. 123
4.5 Monotonicity of Discrete-Time Linear Nonnegative
Dynamical Systems ........................................ 127
4.6 Monotonicity of Discrete-Time Nonlinear Nonnegative
Dynamical Systems ........................................ 132
4.7 Monotonicity of Nonnegative Dynamical Systems
with Time Delay .......................................... 135
Chapter 5. Dissipativity Theory for Nonnegative Dynamical
Systems ........................................... 143
5.1 Introduction ............................................. 143
5.2 Dissipativity Theory for Nonnegative Dynamical Systems ... 145
5.3 Feedback Interconnections of Nonnegative Dynamical
Systems .................................................. 153
5.4 Dissipativity Theory for Nonlinear Nonnegative
Dynamical Systems ........................................ 158
5.5 Feedback Interconnections of Nonnegative Nonlinear
Dynamical Systems ........................................ 164
5.6 Dissipativity Theory for Discrete-Time Nonnegative
Dynamical Systems ........................................ 166
5.7 Specialization to Discrete-Time Linear Nonnegative
Dynamical Systems ........................................ 173
5.8 Feedback Interconnections of Discrete-Time Nonnegative
Dynamical Systems ........................................ 177
5.9 Dissipativity Theory for Nonnegative Dynamical Systems
with Time Delay .......................................... 183
5.10 Feedback Interconnections of Nonnegative Dynamical
Systems with Time Delay .................................. 188
5.11 Dissipativity Theory for Discrete-Time Nonnegative
Dynamical Systems with Time Delay ........................ 191
5.12 Feedback Interconnections of Discrete-Time Nonnegative
Dynamical Systems with Time Delay ........................ 194
Chapter 6. Hybrid Nonnegative and Compartmental Dynamical
Systems ........................................... 197
6.1 Introduction ............................................. 197
6.2 Stability Theory for Nonlinear Hybrid Nonnegative
Dynamical Systems ........................................ 199
6.3 Hybrid Compartmental Dynamical Systems ................... 203
6.4 Dissipativity Theory for Hybrid Nonnegative Dynamical
Systems .................................................. 207
6.5 Specialization to Linear Impulsive Dynamical Systems ..... 215
6.6 Feedback Interconnections of Nonlinear Hybrid
Nonnegative Dynamical Systems ............................ 217
Chapter 7. System Thermodynamics, Irreversibility, and Time
Asymmetry .......................................... 223
7.1 Introduction ............................................. 223
7.2 Dynamical System Model ................................... 226
7.3 Reversibility, Irreversibility, Recoverability, and
Irrecoverability ......................................... 228
7.4 Reversible Dynamical Systems, Volume-Preserving Flows,
and Poincaré Recurrence .................................. 233
7.5 System Thermodynamics .................................... 243
7.6 Entropy and Irreversibility .............................. 247
7.7 Semistability and the Entropic Arrow of Time ............. 254
7.8 Monotonicity of System Energies in Thermodynamic
Processes ................................................ 259
Chapter 8. Finite-Time Thermodynamics ........................ 263
8.1 Introduction ............................................. 263
8.2 Finite-Time Semistability of Nonlinear Nonnegative
Dynamical Systems ........................................ 264
8.3 Homogeneity and Finite-Time Semistability ................ 268
8.4 Finite-Time Energy Equipartition in Thermodynamic
Systems .................................................. 275
Chapter 9. Modeling and Analysis of Mass-Action Kinetics ..... 281
9.1 Introduction ............................................. 281
9.2 Reaction Networks ........................................ 282
9.3 The Law of Mass Action and the Kinetic Equations ......... 284
9.4 Nonnegativity of Solutions ............................... 288
9.5 Realization of Mass-Action Kinetics ...................... 290
9.6 Reducibility of the Kinetic Equations .................... 293
9.7 Stability Analysis of Linear and Nonlinear Kinetics ...... 297
9.8 The Zero-Deficiency Theorem .............................. 301
Chapter 10. Semistability and State Equipartition of
Nonnegative Dynamical Systems ..................... 315
10.1 Introduction ............................................. 315
10.2 Semistability and State Equipartitioning ................. 315
10.3 Semistability and Equipartition of Linear Compartmental
Systems with Time Delay .................................. 324
10.4 Semistability and Equipartition of Nonlinear
Compartmental Systems with Time Delay .................... 328
Chapter 11. Robustness of Nonnegative Dynamical Systems ....... 343
11.1 Introduction ............................................. 343
11.2 Nominal System Model ..................................... 343
11.3 Semistability and Homogeneous Dynamical Systems .......... 347
11.4 Uncertain System Model ................................... 348
Chapter 12. Modeling and Control for Clinical Pharmacology .... 359
12.1 Introduction ............................................. 359
12.2 Pharmacokinetic Models ................................... 360
12.3 State Space Models ....................................... 361
12.4 Drug Action, Effect, and Interaction ..................... 362
12.5 Pharmacokinetic Parameter Estimation ..................... 363
12.6 Pharmacodynamic Models ................................... 365
12.7 Open-Loop Drug Dosing .................................... 366
12.8 Closed-Loop Drug Dosing .................................. 368
12.9 Closed-Loop Control of Cardiovascular Function ........... 369
12.10 Closed-Loop Control of Anesthesia ....................... 371
12.11 Electroencephalograph-Based Control ..................... 372
12.12 Bispectral Index-Based Control .......................... 373
12.13 Pharmacokinetic and Pharmacodynamic Models for Drug
Distribution ............................................ 374
12.14 Challenges and Opportunities in Pharmacological
Control ................................................. 377
Chapter 13. Optimal Fixed-Structure Control for Nonnegative
Systems ........................................... 379
13.1 Introduction ............................................. 379
13.2 Optimal Zero Set-Point Regulation for Nonnegative
Dynamical Systems ........................................ 379
13.3 Optimal Nonzero Set-Point Regulation for Nonnegative
Dynamical Systems ........................................ 383
13.4 Suboptimal Control for Nonnegative Dynamical Systems ..... 390
13.5 Optimal Fixed-Structure Control for Nonnegative
Dynamical Systems ........................................ 392
13.6 Nonnegative Control for Nonnegative Dynamical Systems .... 394
13.7 Optimal Fixed-Structure Control for General Anesthesia ... 396
Chapter 14.H2Suboptimal Control for Nonnegative Dynamical
Systems Using Linear Matrix Inequalities ........... 405
14.1 Introduction ............................................. 405
14.2 H2 Suboptimal Control for Nonnegative Dynamical
Systems .................................................. 405
14.3 Suboptimal Estimation for Nonnegative Dynamical
Systems .................................................. 413
14.4 Hi Suboptimal Dynamic Controller Design for Nonnegative
Dynamical Systems ........................................ 418
Chapter 15. Adaptive Control for Nonnegative Systems .......... 425
15.1 Introduction ............................................. 425
15.2 Adaptive Control for Linear Nonnegative Uncertain
Dynamical Systems ........................................ 427
15.3 Adaptive Control for Linear Nonnegative Dynamical
Systems with Nonnegative Control ......................... 435
15.4 Adaptive Control for General Anesthesia: Linear Model .... 438
15.5 Adaptive Control for Nonlinear Nonnegative Uncertain
Dynamical Systems ........................................ 444
15.6 Adaptive Control for General Anesthesia: Nonlinear
Model .................................................... 451
15.7 Adaptive Control for Nonlinear Nonnegative Uncertain
Dynamical Systems ........................................ 454
15.8 Adaptive Control for Linear Nonnegative Uncertain
Dynamical Systems with Time Delay ........................ 463
15.9 Adaptive Control for Linear Nonnegative Dynamical
Systems with Nonnegative Control and Time Delay .......... 476
15.10 Adaptive Control for Nonnegative Systems with Time
Delay and Actuator Amplitude Constraints ................ 480
15.11 Adaptive Control for General Anesthesia: Linear Model
with Time Delay and Actuator Constraints ................ 484
Chapter 16. Adaptive Disturbance Rejection Control for
Compartmental Systems ............................. 491
16.1 Introduction ............................................. 491
16.2 Compartmental Systems with Exogenous Disturbances ........ 492
16.3 Adaptive Control for Linear Compartmental Uncertain
Systems with Exogenous Disturbances ...................... 493
16.4 Adaptive Control for Linear Compartmental Dynamical
Systems with  2 Disturbances ............................. 502
16.5 Adaptive Control for Automated Anesthesia with
Hemorrhage and Hemodilution Effects ...................... 512
Chapter 17. Limit Cycle Stability Analysis and Control
for Respiratory Compartmental Models .............. 523
17.1 Introduction ............................................. 523
17.2 Ultrametric Matrices, Periodic Orbits, and Poincare
Maps ..................................................... 524
17.3 Compartmental Modeling of Lung Dynamics: Dichotomy
Architecture ............................................. 528
17.4 State Space Multicompartment Lung Model .................. 531
17.5 Limit Cycle Analysis of the Multicompartment Lung
Model .................................................... 534
17.6 A Regular Dichotomy Model ................................ 538
17.7 A General Tree Structure Model ........................... 541
17.8 Direct Adaptive Control for Switched Linear Time-
Varying Systems .......................................... 545
17.9 Adaptive Control for a Multicompartment Lung Model ....... 548
Chapter 18. Identification of Stable Nonnegative and
Compartmental Systems ............................. 553
18.1 Introduction ............................................. 553
18.2 State Reconstruction ..................................... 554
18.3 Constrained Optimization for Subspace Identification of
Stable Nonnegative Systems ............................... 557
18.4 Constrained Optimization for Subspace Identification of
Compartmental Systems .................................... 566
18.5 Illustrative Numerical Examples .......................... 567
Chapter 19. Conclusion ........................................ 571
Bibliography .................................................. 573
Index ......................................................... 599
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