Algebraic necessary and sufficient condition for difference flatness

ABSTRACT

In this paper, a novel solution is proposed for verifying difference flatness of a nonlinear discrete-time control system. A necessary and sufficient condition is proved under which a discrete-time control system is flat. The condition is based on a sequence of vector spaces of differential 1-forms. A more general definition of flatness is considered than in most cases, since the flat output is allowed to depend on the backward shifts of the states and inputs. Also, unlike most conditions that check flatness of a discrete-time system, the one proposed in the current paper does not require actually computing the flat output. Although, the flat output can be found from the vector spaces based on which the necessary and sufficient condition is presented. Algorithms are provided in order to compute all the necessary vector spaces. Two examples illustrate the results.

KEYWORDS:

• Nonlinear control systems
• discrete-time systems
• difference flatness
• algebraic methods

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Estonian Research Council [grant number PSG424].