摘要：In this paper we study feedback linearization of multi-input control-affine systems via a particular class of nonregular feedback transformations, namely by reducing the number of controls by one. A complete geometric characterization of systems of that class requires special properties of the linearizability distributionsƊ0⊂Ɗ1⊂Ɗ2⊂⋯. Contrary to the case of regular feedback linearization, they need not be involutive but the first noninvolutive one has to contain a sufficiently large involutive subdistribution. Recently, we solved the problem ofƊ0being noninvolutive. In the present paper, we study the case ofƊ0involutive butƊ1noninvolutive. This case is specially interesting because it covers a big class of mechanical control systems. We provide geometric necessary and sufficient conditions describing our class of systems that can be verified by differentiation and algebraic operations only. We illustrate our results by several examples and discuss relations with other linearizability problems (static invertible feedback linearization or dynamic linearization).
