A Structurally Flat Triangular Form for Three-Input Systems

TL;DR

This paper introduces a new structurally flat triangular form for three-input control-affine systems, providing conditions for feedback equivalence and flatness, enhancing control system analysis and design.

Contribution

It defines a novel triangular form for three-input flat systems, with conditions for feedback equivalence and methods for transforming general systems into this form.

Findings

Derived necessary and sufficient conditions for feedback equivalence.

Presented conditions for transforming systems into the triangular form after input prolongations.

Established regularity conditions ensuring structural flatness.

Abstract

We present a broadly applicable structurally flat triangular form for x-flat control-affine systems with three inputs. Building on recent results for the derivative structure of flat outputs, we define the triangular form together with regularity conditions that guarantee structural flatness, and derive necessary and sufficient conditions for a system with a given x-flat output to be static feedback equivalent to this form. Further, we present sufficient conditions under which general x-flat three-input systems can be rendered static feedback equivalent to the proposed triangular form after a finite number of input prolongations.