# On Measures of Non-Integrability of Pfaffian Systems

From MurrayWiki

### Andrjez Banaszuk, John Hauser, Willem Sluis, Richard M. Murray

IFAC World Congress, July 1996

Many problems in nonlinear control theory (like, for instance, feedback linearization problem) lead to examination of integrability of a Pfaffian system. In a generic case a Pfaffian system is not integrable. Therefore, how to approximate nonintegrable Pfaffian systems by integrable ones and how this approximation can be applied in practice appears to be a natural and important problem. In the present paper we establish some measures of non-integrability of Pfaffian system of arbitrary dimension and discuss their relation to approxiations of non-integrable Pfaffian systems by integrable ones. Our work is motivated by expected applications to approximate feedback linearization of multi-input nonlinear systems.