Comments on "A Controllability Counterexample" and the Continuation Lemma

Comments on "A Controllability Counterexample" and the Continuation Lemma

A Technical Note in this journal vol. 50, no. 6, pp. 840-841, June 2005, by Elliott, gives a bilinear example showing that the Euler discretization of a noncontrollable continuous-time system can be controllable. The example is correct, but there was a flaw in a result of the TN, Lemma 1 ("for...

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Veröffentlicht in:IEEE transactions on automatic control 2015-04, Vol.60 (4), p.1169-1171
Hauptverfasser: Elliott, David L., Lin Tie
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Controllability
Discrete-time systems
Nonlinear systems
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Lin Tie
description A Technical Note in this journal vol. 50, no. 6, pp. 840-841, June 2005, by Elliott, gives a bilinear example showing that the Euler discretization of a noncontrollable continuous-time system can be controllable. The example is correct, but there was a flaw in a result of the TN, Lemma 1 ("for discrete-time systems, local controllability implies controllability") that has independent interest. In this note, the lemma is reformulated as a conjecture for continuous-in-state systems, and it is also proved under additional conditions. For a class of two-dimensional bilinear systems the Euler discretization is shown directly to be small-controllable, a fortiori controllable.
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Nonlinear systems
title Comments on "A Controllability Counterexample" and the Continuation Lemma
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