랴푸노프 안정성

노트

위키데이터

• ID : Q1341651

말뭉치

1. The Lyapunov stability is a method that was developed for analysis purposes.
2. The Lyapunov stability theory can be generalized as follows.
3. ( x ) using the Lyapunov function method.
4. Notice that, for small systems, the construction of the Lyapunov function can be done manually.
5. This may be discussed by the theory of Aleksandr Lyapunov.
6. The mathematical theory of stability of motion, founded by A. M. Lyapunov, considerably anticipated the time for its implementation in science and technology.
7. Moreover Lyapunov did not himself make application in this field, his own interest being in the stability of rotating fluid masses with astronomical application.
8. More recently the concept of the Lyapunov exponent (related to Lyapunov's First Method of discussing stability) has received wide interest in connection with chaos theory.
9. The case represented by inequality (15b) was called by Lyapunov a “critical” case.
10. From the preceding definitions it follows that Lyapunov stability is only meaningful for solutions of ordinary differential equations.
11. Lyapunov stability of a point relative to a mapping is defined as Lyapunov stability relative to the family of non-negative powers of this mapping.
12. (Lyapunov's theorem on stability in a first approximation); to facilitate the verification of the condition in this theorem one applies criteria for stability.
13. For the study of stability in critical cases, A.M. Lyapunov proposed the so-called second method for studying stability (cf.
14. In automatic control, the main interest of the Lyapunov approach concerns the stability analysis of nonlinear systems.
15. This chapter provides an introduction to the Lyapunov stability of nonlinear fractional systems.
16. The introduction begins with the indirect Lyapunov method, based on a local approximation around the equilibrium point, which makes it possible to test system local stability.
17. The variable gradient method makes it possible to build a Lyapunov function.
18. A Lyapunov function is a scalar function defined on the phase space, which can be used to prove the stability of an equilibrium point.
19. The Lyapunov function method is applied to study the stability of various differential equations and systems.
20. Thus, Lyapunov functions allow to determine the stability or instability of a system.
21. The disadvantage is that there is no general method of constructing Lyapunov functions.
22. The stability of the proposed controller is proven by applying Lyapunov stability theory.
23. We present a Lyapunov-type approach and the Lyapunov-Floquet (L-F) transformation to derive the stability conditions.
24. It makes use of a Lyapunov function .
25. For a linear system with constant coefficients, it is rather simple to find a Lyapunov function.
26. Equation (2.7) is called the Lyapunov equation.
27. (17) to remain stable only for certain values of d and it appears to be much more difficult to find Lyapunov functionals that yield stability criteria.
28. Therefore, we start with the Laplace transform method to find sufficient conditions for stability and try to find similar conditions with the help of a Lyapunov functional.
29. (17), from which we retrieve a Lyapunov functional in Section 4.5.2.