| Discrete-time transitivity and accessibility: analytic systems (1993) | |||||||||||||||||
Abstract | |||||||||||||||||
| A basic open question for discrete-time nonlinear systems is that of determining when, in analogy with the classical continuous-time “positive form of Chow’s Lemma,” accessibility follows from transitivity of a natural group action. This paper studies the problem, and establishes the desired implication for analytic systems in several cases: (i) compact state space, (ii) under a Poisson stability condition, and (iii) in a generic sense. In addition, the paper studies accessibility properties of the “controllability sets ” recently introduced in the context of dynamical systems studies. Finally, various examples and counterexamples are provided relating the various Lie algebras introduced in past work. | |||||||||||||||||
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