| | |
| | |
Stat |
Members: 3645 Articles: 2'501'711 Articles rated: 2609
19 April 2024 |
|
| | | |
|
Article overview
| |
|
Further Results on Lyapunov-Like Conditions of Forward Invariance and Boundedness for a Class of Unstable Systems | A.N. Gorban
; I.Yu. Tyukin
; H. Nijmeijer
; | Date: |
1 Dec 2014 | Abstract: | We provide several characterizations of convergence to unstable equilibria in
nonlinear systems. Our current contribution is three-fold. First we present
simple algebraic conditions for establishing local convergence of non-trivial
solutions of nonlinear systems to unstable equilibria. The conditions are based
on the earlier work (A.N. Gorban, I.Yu. Tyukin, E. Steur, and H. Nijmeijer,
SIAM Journal on Control and Optimization, Vol. 51, No. 3, 2013) and can be
viewed as an extension of the Lyapunov’s first method in that they apply to
systems in which the corresponding Jacobian has one zero eigenvalue. Second, we
show that for a relevant subclass of systems, persistency of excitation of a
function of time in the right-hand side of the equations governing dynamics of
the system ensure existence of an attractor basin such that solutions passing
through this basin in forward time converge to the origin exponentially.
Finally we demonstrate that conditions developed in (A.N. Gorban, I.Yu. Tyukin,
E. Steur, and H. Nijmeijer, SIAM Journal on Control and Optimization, Vol. 51,
No. 3, 2013) may be remarkably tight. | Source: | arXiv, 1412.0524 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |