Bifurcations of 1-parameter families of control-affine systems in the plane

We define bifurcations of control-affine systems in the plane and classify all generic 1-parameter bifurcations at control-regular points. More precisely, we classify topological bifurcations of invariants of usual feedback equivalence. Such bifurcations form six different classes: two bifurcations...

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Bibliographic Details
Published in:SIAM journal on control and optimization 2006, Vol.44 (6), p.2038-2062
Main Authors: JAKUBCZYK, Bronislaw, RESPONDEK, Witold
Format: Article
Language:English
Subjects:
Applied mathematics
Applied sciences
Computer science
control theory
systems
Control theory. Systems
Equilibrium
Exact sciences and technology
System theory
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Summary:We define bifurcations of control-affine systems in the plane and classify all generic 1-parameter bifurcations at control-regular points. More precisely, we classify topological bifurcations of invariants of usual feedback equivalence. Such bifurcations form six different classes: two bifurcations of equilibrium sets, two bifurcations of critical sets, and two bifurcations of pairs of invariants. We also classify all generic 1-parameter families of control-affine systems with respect to orbital feedback equivalence.
ISSN:0363-0129
1095-7138
DOI:10.1137/S0363012903431165