Abstract
We consider local feedback equivalence of control-affine systems in the plane. We present a general normal form for such systems with scalar control. In this form a polynomial of one variable appears, with coefficients which are functions of another variable. We show that these coefficients (called functional parameters) are invariants. This gives a complete feedback classification of planar systems. The classification results are stated separately for nonequilibrium and equilibrium points. The functional invariants which appear in the normal form have a direct interpretation in terms of singular, time-extremal trajectories of the systems. We show that, roughly, the singular extremals determine the functional invariants of the system and vice versa.
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© 1991 Birkhäuser Boston
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Jakubczyk, B., Respondek, W. (1991). Feedback Classification of Analytic Control Systems in the Plane. In: Bonnard, B., Bride, B., Gauthier, JP., Kupka, I. (eds) Analysis of Controlled Dynamical Systems. Progress in Systems and Control Theory, vol 8. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3214-8_23
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DOI: https://doi.org/10.1007/978-1-4612-3214-8_23
Publisher Name: Birkhäuser Boston
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