Analytical Methods for Studying the Stability of Linear and Quasi-Linear Systems with Polynomial Completeness of the Periodic Matrix

We propose a method for the analysis of linear and quasi-linear model systems of ordinary differential equations (ODE) with polynomially periodic matrix in the presence of A0(t) defining different stable Jordan structure. With the help of a modern method of splitting algorithm (proposed in the nineties of the twentieth century), the new above mentioned classes of systems of ordinary differential equations are studied and a number of non-trivial theorems on reducibility to an equivalent system with an almost diagonal matrix are made, allowing sufficient conditions for the stability of solutions of such systems. The developed method is given the opportunity to explore a number of application-specific modeling problems that generalizes and refines the known results.

модельные системы обыкновенных дифференциальных уравнений с полиномиально периодической матрицей, метод расщепления, устойчивость, теоремы о приводимости