Stability of Motion: Applications of Lyapunov's Second Method to Differential Systems and Equations With Delay

Cover......Page 1
Title......Page 4
Contents......Page 6
Introduction......Page 10
2. Preliminary remarks,......Page 20
3. Some useful lemmas,......Page 21
4. Conditions for the existence of a Lyapunov function having a derivative dv/dt of definite sign,......Page 25
5. Theorems on the existence of a Function v(x,t) that satisfies the conditions of Lyapunov\'s theorem on asymptotic stability,......Page 34
6. Theorems on the existence of a Function v[x,t) that Satisfies the conditions of Lyapunov\'s first theorem on instability,......Page 44
7. Theorems on the existence of a Function v(x,t) that Satisfies the conditions of Lyapunov\'s second theorem on instability, or Cetaev\'s theorem on instability,......Page 48
9. Uniform nonasymptotic stability,......Page 53
10. Generalizations of Lyapunov\'s theorems on asymptotic stability when Stability is Nonuniform,......Page 62
11. Lyapunov functions that satisfy estimates given in terms of quadratic forms,......Page 66
12. Modification of Cetaev\'s theorem on instability,......Page 72
14. Criteria for asymptotic stability,......Page 75
15. Sufficient criteria for instability,......Page 77
16. Criteria for stability with respect to large initial perturbations, based on Lyapunov\'s theory of stability of the perturbed trajectory,......Page 79
17. Some Complements to the Theorems of Lyapunov,......Page 85
18. Preliminary remarks,......Page 89
19. Structural stability and instability,......Page 90
20. Criteria for Asymptotic Stability of Quasi-linear Systems,......Page 95
21. Sufficient conditions for the asymptotic stability of solutions of nonlinear systems of differential equations,......Page 99
22. Theorems on n-order stability,......Page 103
23. Preliminary Remarks,......Page 107
24. Stability for Persistent Disturbances that are Bounded in the Mean,......Page 109
25. Criteria for Asymptotic Stability in the Large for Some Nonlinear Systems,......Page 118
26. Singular Cases,......Page 132
27. Preliminary Remarks,......Page 135
28. Statement of the Stability Problem for Equations with Time Delay,......Page 139
29. Stability of Linear Systems of Equations with Time Delay,......Page 142
30. Fundamental definitions and theorems of Lyapunov\'s second method or equations with time delay,......Page 152
31. Some sufficient conditions for asymptotic stability of equations with time delay,......Page 160
32. Stability for Persistent Disturbances,......Page 170
33. First-order Stability for Equations with Time Delay,......Page 173
34. Construction of Functionals in Special Cases,......Page 178
References,......Page 186
Index,......Page 196