Abstract
Many paper's devoted to nonlinear control systems have been appeared during latest decades. Powerful methods based on defferential geometry, topology and algebra are developed now. Nevertheless a lot of nonlinear control problems are waiting to be thoroughly researched in near future. That is such wide range ot tasks as for example: analysis of both local and global controllability; stabilizability and stabilizer's design; observability, observer's design and application to stabilizability; realization and so on. Partly we are able to solve some of the problems mentioned above. We would like to submit a paper devoted to nonlinear Cronekker's characteristics and its application. In the paper we introduce nonlinear analog of Cronekker's invariant well-lsnown in linear control theory. The new concept induces us to develop new tools for nonlinear control system research. Using the tools wich are turned out very effective we have succeeded in obtaining new results on global and local controllability, stability and stabilizability of nonlinear systems. For instance we have found geometrical sufficient conditions for a nonlinear system with non asymptoticaly stable linearization to be locally stable, proposed the new stabilizer design procedure for conservative systems with deay, generalized Kunita's results concerning nonlinear controllability.
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