| Further Results on Controllability Properties of Discrete-Time Nonlinear Systems (1994) | |||||||||||||||
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| Controllability questions for discrete-time nonlinear systems are addressed in this paper. In particular, we continue the search for conditions under which the group-like notion of transitivity implies the stronger and semigroup-like property of forward accessibility. We show that this implication holds, pointwise, for states which have a weak Poisson stability property, and globally, if there exists a global "attractor" for the system. 1 Introduction This paper continues the study, initiated in [4] and then developed in [1], of some controllability properties of discrete-time nonlinear systems, of the type: x(t + 1) = f(x(t); u(t)); t = 0; 1; 2; : : : ; (1) where x(t) 2 X and u(t) 2 U . We will deal, as in the above-mentioned papers, with the class of invertible systems, that is with those systems for which the function f(1; u) is a diffeomorphism. Such systems arise, for instance, when dealing with continuous-time models under digital controls via sampling. For futher motivations o... | |||||||||||||||
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