This paper develops a constructive method for nding a nilpotent basis for a special class of smooth nonholonomic distributions. The main tool is the use of the Goursat normal form theorem which arises in the study of exterior di erential systems. The results are applied to the problem of nding a set of nilpotent input vector elds for a nonholonomic control system, which can then used to constru...

We consider linear 2-D systems of Fornasini-Marchesini type in the continuous-time case with non-constant coefficients. Using an explicit representation of the solutions by utilizing the Riemann-kernel of the equation under consideration, we obtain controllability and observability criteria in the case of the inhomogeneous equation, where control is obtained by choosing the inhomogeneity approp...

Let V be a vector field distribution on manifold M . We give an efficient algorithm for the construction of local coordinates on M such that V may be locally expressed as some partial prolongation of the contact distribution C (1) q , on the 1 st order jet bundle of maps from R to R, q ≥ 1. It is proven that if V is locally equivalent to a partial prolongation of C (1) q then the explicit const...

We provide necessary and sufficient conditions on the derived type of a vector field distribution V in order that it be locally equivalent to a partial prolongation of the contact distribution C (1) q , on the 1 order jet bundle of maps from R to R, q ≥ 1. This result fully generalises the classical Goursat normal form. Our proof is constructive: it is proven that if V is locally equivalent to ...

Complex variable method (Cauchy integral method) has been applied to derive exact and closed expressions of Goursat functions for the first and second fundamental problems for an infinite plate weakened by a curvilinear hole. The area outside the hole with the hole itself is conformally mapped on the right half-plane by the use of a rational mapping function. This rational mapping consists of c...