Abstract
For discrete-time nonlinear systems, this paper provides new conditions under which it can be proved that transitivity implies forward accessibility. Assuming that the system is analytic, it is shown that the implication holds if the state-space is compact, or if a Poisson stability condition is satisfied, and also that the result holds in a generic sense. Various examples and counterexamples are provided relating the dimensions of the accessibility and transitivity Lie algebras.
This research was supported in part by US Air Force Grant AFOSR-88-0235.
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© 1991 Birkhäuser Boston
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Albertini, F., Sontag, E.D. (1991). Transitivity and Forward Accessibility of Discrete-Time Nonlinear Systems. 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_3
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DOI: https://doi.org/10.1007/978-1-4612-3214-8_3
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-7835-1
Online ISBN: 978-1-4612-3214-8
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