Shevlyakov

For nonlinear dynamical systems with scalar control the equilibrium point stabilization problem is considered using a transformation of the system in a regular quasicanonical form.  Affine systems are investigated which can be transformed to quasicanonical form with  transformability index greater then two.   Zero dynamics of the system are not asymptotically stable.  The virtual outputs method of stabilizing  feedback design is propagated on the above mentioned systems.

A problem of finding rank of non-square functional matrix, whose elements are smooth functions, is considered. Such matrices arise in course of analysis of regularity and involutivity of vector distributions. To find rank of these matrices, it is convenient to use computer algebra systems, which can perform symbolic computations. Alternative to checking all possible minors is the Gauss algorithm of transforming matrix to row-echelon form. When considering regularity and involutivity, it is often of interest to know the rank of a matrix in the neighborhood of a point. Usual Gauss algorithm cannot answer this question, since it is possible for basis minor to become zero at chosen point.  A modified algorithm is presented. This algorithm allows to say if there exists a neighborhood of constant rank containing a chosen point. Examples are presented.