Abstract
For most nonlinear systems, it is in general a difficult task to obtain algebraic controllability criteria. In this paper, we consider small-controllability of discrete-time state-affine nonlinear systems. We first focus on the systems in dimension two with single-input and improve a previous controllability criterion. That is, we derive a sufficient algebraic criterion for small-controllability of the systems, which is easier to apply than the previous one. We then show that if the state-affine nonlinear systems are bilinear, a necessary and sufficient algebraic criterion for small-controllability can be obtained using invariant sets. We also extend the derived controllability criteria to continuous-time state-affine nonlinear systems and to discrete-time multi-input state-affine nonlinear systems. Examples are given to illustrate the derived controllability criteria of this paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Correction Statement
This article has been republished with minor changes. These changes do not impact the academic content of the article.
Notes
1 Here, A can always be put in canonical form by a nonsingular linear transformation P. Similarly,
and
. From Definition 2.1, this transformation does not affect the small-controllability.