Dynamic feedback linearization of two-input control systems via successive one-fold prolongations

In this paper, we propose a constructive algorithm to dynamically linearize two-input control systems via successive one-fold prolongations of a control that has to be suitably chosen at each step of the algorithm. Contrary to the case of static feedback linearization, for linearization via successive one-fold prolongations, the linearizability distributions need not be involutive but the first noninvolutive one has to contain a sufficiently large involutive subdistribution. The main idea of the algorithm is, at each new step, to prolong the system in such a way that the first noninvolutive distribution is replaced by its largest involutive subdistribution, thus for the prolonged system we gain at least one new involutive distribution. Our algorithm is constructive, gives sufficient conditions for flatness, and can be seen as the dual of the dynamic feedback linearization algorithm of Battilotti and Califano [1], [4], which is also based on prolongations, but for which the to-be-prolonged control is identified with the help of the last noninvolutive linearizability distribution.