Special matrix transformations of essential nonlinear control systems

Complex nonlinear control systems that are fundamentally non-linearizable (containing, for example, ambiguous nonlinearities), as a rule, can not be fully investigated analytically. On the other hand, the use of only computer technologies for their research often gives rise to doubts about the reliability of the results obtained. Therefore, methods based on the decomposition of the space of parameters of essentially nonlinear multidimensional systems acquire special significance. Describe the method for finding the matrix of a canonical transformation, under which the matrix of the linear part of the original system is reduced to the first natural normal form.