An algorithm for orbital feedback linearization of single-input control affine systems

Abstract

Feedback linearization is an effective design and analysis tool used in the study of nonlinear control systems. However, cases arise where linearizability conditions cannot be met. For systems that are not linearizable by classical techniques, orbital feedback linearization (or feedback linearization by state-dependent time scaling) has been proposed to relax these conditions. Unfortunately, approaches proposed to date have led to conditions that tend to be more difficult to check then conditions for state-feedback linearization. In this paper, necessary and sufficient conditions for orbital feedback linearizability is presented for a class of single-input nonlinear systems. The conditions are simple and can be checked directly from the data of the problem. Using an exterior calculus approach, a simple algorithm is developed to compute state-dependent time scaling that yield state-feedback linearizable systems. It is shown that orbital feedback linearizability generalizes the concept state-feedback linearizability to deal with locally weakly accessible control systems. © 1999 Elsevier Science B.V. All rights reserved.