Practical stability of nonlinear systems

Table of contents ......Page 3
Copyright ......Page 4
Contents vii ......Page 7
Preface v ......Page 5
1.0. Introduction 1 ......Page 10
1.1. Definitions of Lyapunov stability 2 ......Page 11
1.2. Definitions of practical stability 8 ......Page 17
1.3. Stability criteria 12 ......Page 21
1.4. Delay differential equations 22 ......Page 31
1.5. Integro-differential equations 26 ......Page 35
1.6. Difference equations 30 ......Page 39
1.7. Impulsive differential equations 40 ......Page 49
1.8. Notes 51 ......Page 60
2.0. Introduction 53 ......Page 62
2.1. Basic comparison theorems 54 ......Page 63
2.2. Stability criteria 59 ......Page 68
2.3. Perturbing Lyapunov functions 70 ......Page 79
2.4. Several Lyapunov functions 74 ......Page 83
2.5. Large scale dynamic systems 77 ......Page 86
2.6. General definitions of practical stability 80 ......Page 89
2.7. Stability criteria in terms of two measures 84 ......Page 93
2.8. Global results in terms of sets 91 ......Page 100
2.9. Stability criteria in terms of sets 97 ......Page 106
2.10. Notes 101 ......Page 110
3.0. Introduction 103 ......Page 112
3.1. Stability of perturbed systems 104 ......Page 113
3.2. Stability of perturbed systems (continued) 108 ......Page 117
3.3. A technique in perturbation theory 111 ......Page 120
3.4. Difference equations 119 ......Page 128
3.5. Delay differential equations 122 ......Page 131
3.6. Integro-differential equations of Volterra type 127 ......Page 136
3.7. Impulsive differential systems 131 ......Page 140
3.8. Impulsive integro-differential equations 138 ......Page 147
3.9. Reaction-diffusion equations 145 ......Page 154
3.10. Notes 155 ......Page 164
4.0. Introduction 157 ......Page 166
4.1. Control systems 158 ......Page 167
4.2. Controllable systems 164 ......Page 173
4.3. Decentralized control systems 169 ......Page 178
4.4. Optimal controllability 173 ......Page 182
4.5. Set-valued differential inequalities 177 ......Page 186
4.6. Practical stability criteria 182 ......Page 191
4.7. Notes 186 ......Page 195
A.I. Differential inequalities 189 ......Page 198
A.2. Integro-differential equations 195 ......Page 204
A.3. Impulsive differential inequalities 196 ......Page 205
References 199 ......Page 208
cover......Page 1
back cover ......Page 217