| Introduction | p. 1 |
| Lurie Control System | p. 1 |
| Lurie Absolute Stability and Lyapunov Stability | p. 2 |
| Recent Development of Absolute Stability Theory in New Areas | p. 3 |
| The Lurie Problem | p. 4 |
| The Aizerman Problem and Aizerman Conjecture | p. 4 |
| Modern Mathematical Tools for Absolute Stability | p. 6 |
| Principal Theorems on Global Stability | p. 7 |
| Lyapunov Function and K-Class Function | p. 7 |
| Dini Derivative | p. 9 |
| M-Matrix, Hurwitz Matrix, Positive (Negative) Definite Matrix | p. 12 |
| Principal Theorems on Global Stability | p. 16 |
| Global Stability | p. 16 |
| Partial Global Stability | p. 19 |
| Global Stability of Sets | p. 20 |
| Nonautonomous Systems | p. 22 |
| Systems with Separable Variables | p. 23 |
| Autonomous Systems with Generalized Separable Variables | p. 30 |
| Nonautonomous Systems with Separable Variables | p. 32 |
| Sufficient Conditions of Absolute Stability: Classical Methods | p. 37 |
| Absolute Stability of Lurie Control System | p. 37 |
| Lyapunov-Lurie Function Method | p. 42 |
| Lyapunov-Lurie Type V-Function Method Plus S-Program | p. 44 |
| Several Equivalent SANC for Negative Definite Derivatives | p. 46 |
| Popov Frequency Criterion | p. 53 |
| The Classical Popov Criterion | p. 53 |
| The Simplified Popov Criterion | p. 58 |
| Necessary and Sufficient Conditions for Absolute Stability | p. 65 |
| Necessary and Sufficient Conditions for Absolute Stability | p. 65 |
| Lurie Direct Control Systems | p. 76 |
| The S-Method and Modified S-Method | p. 85 |
| The S-Method | p. 85 |
| The Modified S-Method | p. 87 |
| Lurie Indirect Control System | p. 90 |
| Lurie Systems with Loop Feedbacks | p. 101 |
| Special Lurie-Type Control Systems | p. 113 |
| Three Special Order Control Systems | p. 113 |
| The Second-Order Direct Control Systems | p. 113 |
| A Class of the Third-Order Control Systems | p. 116 |
| Special nth-Order Direct Control Systems | p. 116 |
| The First Canonical Form of Control Systems | p. 122 |
| Critical Systems | p. 124 |
| The Second Canonical Form of Control Systems | p. 127 |
| Two Special Systems | p. 130 |
| The Systems with A[superscript T] A = AA[superscript T], A[superscript T] = A, or A + A[superscript T] = -2[rho]E | p. 134 |
| Nonautonomous Systems | p. 139 |
| Nonautonomous Systems | p. 139 |
| Systems with Separable Variables | p. 143 |
| Direct Control Systems | p. 147 |
| Indirect Control Systems | p. 148 |
| Systems with Loop Revolving Feedbacks | p. 152 |
| Systems with Multiple Nonlinear Feedback Controls | p. 157 |
| Necessary and Sufficient Conditions for Absolute Stability | p. 157 |
| Some Simple Sufficient Conditions for Absolute Stability | p. 165 |
| Special Systems | p. 171 |
| Nonautonomous Systems | p. 173 |
| Lurie Systems with Multiple Nonlinear Loop Feedbacks | p. 178 |
| Robust Absolute Stability of Interval Control Systems | p. 183 |
| Interval Lurie Control Systems | p. 183 |
| Sufficient and Necessary Conditions for Robust Absolute Stability | p. 184 |
| Sufficient Conditions for Robust Absolute Stability | p. 186 |
| Algebraic Sufficient and Necessary Conditions | p. 191 |
| Interval Yocubovich Control Systems | p. 194 |
| SANC for the Robust Absolute Stability of the Interval Yocubovich System (8.19) | p. 196 |
| Sufficient Conditions for the Robust Absolute Stability of System (8.19) | p. 199 |
| Numerical Examples and Simulation Results | p. 210 |
| More General Interval Systems [171, 172] | p. 213 |
| Discrete Control Systems | p. 221 |
| Sufficient and Necessary Conditions for the Absolute Stability | p. 221 |
| Sufficient Algebraic Conditions for the Absolute Stability | p. 227 |
| Discrete Lurie Control Systems with Multiple Loops Feedback | p. 231 |
| Sufficient Conditions for Discrete Control Systems with Loops Feedback | p. 237 |
| Time-Delayed and Neutral Lurie Control Systems | p. 243 |
| Lurie Systems with Constant Time Delays | p. 243 |
| Sufficient and Necessary Conditions for Absolute Stability | p. 243 |
| Algebraic Sufficient Conditions | p. 248 |
| Absolute Stability Based on Partial Variables | p. 253 |
| Lurie Systems with Multiple Time Delays | p. 257 |
| Time-Delay Dependent Absolute Stability of Lurie Systems | p. 264 |
| Neutral Lurie Control Systems | p. 268 |
| Time-Delay Independent Absolute Stability | p. 268 |
| Time-Delay Dependent Absolute Stability | p. 272 |
| Control Systems Described by Functional Differential Equations | p. 279 |
| The Systems Described by RFDE | p. 279 |
| FDE Lurie Systems with Multiple Feedback Controls | p. 288 |
| Large-Scale Control Systems Described by RFDE | p. 292 |
| Systems Described by NFDE | p. 295 |
| Control Systems in Hilbert Spaces | p. 300 |
| Lurie Systems Described by PFDE | p. 306 |
| Absolute Stability of Hopfield Neural Network | p. 313 |
| Hopfield Neural Network | p. 313 |
| Relation and Difference of Hopfield Neural Network and Lurie System | p. 315 |
| Sufficient and Necessary Conditions for Hopfield Neural Network | p. 317 |
| Absolute Stability of Cooperative Hopfield Neural Network | p. 322 |
| Sufficient Conditions for Absolutely Exponential Stability | p. 323 |
| Hopfield Neural Networks with Finite Gains | p. 323 |
| Hopfield Neural Networks with Infinite Gains | p. 327 |
| Absolute Stability of Lurie Discrete Delay Neural Networks | p. 331 |
| Application to Chaos Control and Chaos Synchronization | p. 337 |
| The Relation of Chua's Circuit and Lurie System | p. 337 |
| Globally Exponent Synchronization of Two Chua's Chaotic Circuits | p. 340 |
| Linear Feedback Control | p. 340 |
| Nonlinear Feedback Control | p. 348 |
| Globally Exponential Synchronization w.r.t. Partial State Variables | p. 351 |
| Remarks on Nonsynchronization | p. 353 |
| Numerical Simulation Results | p. 354 |
| Master-Slave Synchronization of Two General Lurie Systems | p. 358 |
| Indirect Feedback Control | p. 358 |
| Time-Delayed Feedback Control | p. 362 |
| References | p. 371 |
| Index | p. 379 |
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