ISSN:
1573-8698
Keywords:
Singular perturbation
;
invariant manifold
;
overflowing manifold
;
stability
;
characteristic numbers
Source:
Springer Online Journal Archives 1860-2000
Topics:
Electrical Engineering, Measurement and Control Technology
Notes:
Abstract A singularly perturbed system with a small parameter ε at the velocity of the slow variable y and with the fast variable x is considered. The main hypothesis is that for all y from some bounded domain D, the fast subsystem has a stable invariant or overflowing manifold M 0(y) and that the motions in this system going in the directions transversal to M 0(y) are more fast than the mutual approaching of trajectories on M 0(y) (a precise statement is given in terms of appropriate Lyapunov-type characteristic numbers). It is proved that for a sufficiently small ε, the whole system has an invariant manifold close to $$\bigcup\limits_{y \in D} {M_0 (y) \times \{ y\}}$$ the degree of its smoothness is specifed.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1021739205527
