THE COMPLETE SOLUTION OF THE GENERAL ROUTH PROBLEM IN SYSTEMS-THEORY .2.

This article examines the complete solution of the general Routh problem as a set of three problems in the algebra of polynomials: the problem of the index of a rational function and the mutuality properties of the polynomials constituting it, the problem of analyzing the distribution of the roots of a polynomial relative to the real axis of the complex plane, and the problem of analyzing the distribution of the roots relative to the imaginary axis. The solution is based on a generalization of Routh's algorithm and method. This generalization makes it possible to obtain solutions of all three problems in a uniform form that is free of critical cases in realizing the algorithms. The complete solution of the general Routh problem enables the effective applications of Routh's method in problems in systems theory considerably to be increased.