Orbital flatness of a class of single-input control systems

Abstract

This paper gives necessary and sufficient conditions describing single-input affine systems that are orbital feedback equivalent to the affine Goursat normal form (AGNF). This class of systems are not differential flat, but they are orbitally flat. A complete characterization of all the orbitally flat output for single-input affine systems that are orbitally feedback equivalent to AGNF are derived. Moreover, we analyze a linear controllable system that is orbital feedback equivalent to AGNF on ℝ3 and describe all the possible time re-scaling functions under which the time scaled system remains differential flat.