A‐Orbital feedback linearization of multiinput control affine systems

Abstract

SummaryThis article deals with transformations of multiinput nonlinear control systems into linear controllable systems. For multiinput control affine systems, the notion of A‐orbital feedback linearizability is introduced which generalizes the notion of orbital feedback linearizability and is based on input‐dependent time scalings. A necessary and sufficient condition for A‐orbital feedback linearizability is derived for multiinput control affine systems. On the basis of this condition, an A‐orbital feedback linearization algorithm is developed. It is revealed that the proposed concept extends the existing approaches to orbital feedback linearization. More precisely, it is proved that if a system is A‐orbitally feedback linearizable in a neighborhood of some point, the dimension of the state is greater than that of the input by at least three, and the time scaling essentially depends on the input, then the system cannot be orbitally feedback linearized around that point.