A way то analyze unambiguity of linear mappings and its application to observability problems

The observability of nonlinear $n$-th. order system is analysed by using Gail and Kikaido's sufficient criteria of 1-1-correspondence which require that the phase region be rectangular and the sign of all $N\gg n$ major minors of the Jakobi matrix be investigated. In the new technique the sufficient (necessary and sufficient) с conditions of 1-1-correspondence are found without constraints on the structure of the region by solving one ($N_1<N$) inequality (or severls inequalities).