EQUIVALENCE OF NONLINEAR-SYSTEMS TO TRIANGULAR FORM - THE SINGULAR CASE

The problem of state equivalence of a given nonlinear system to a tria ngular form is considered here. The solution of this problem has been known for the regular case, i.e. when there exists a certain nested se quence of regular and involutive distributions. It is also known that in this case the corresponding system is linearizable using a smooth c oordinate change and static state feedback. This paper deals with the singular case, i.e. when the nested sequence of involutive distributio ns of the system contains singular distributions. Special attention is paid to the so-called bijective triangular form. Geometric, coordinat es-free criteria for the solution of the above problem as well as cons tructive, verifiable procedures are given. These results are used to o btain a result in the nonsmooth stabilization problem.