There are different criteria for the stability of the solution of linear differential equations which are based on the characteristic equation analysis. In this work the reader will find principally new ways of frequency criteria for stability derivation which are based on Perceval formula and a resolution of operator equations in Banach space.

This book presents the Determinant theory with the use of hypercomplex Grassmann figures. It simplifies the proof of many determinant features. It also states several ways of solutions of linear algebraic systems, most of which are connected with the Determinant theory. The teaching experience in technical universities has demonstrated that the suggested way of presenting the Determinant theory is understood more easily. The title of the book is explained by a desire to attract readers attention to the well-known in the algebra sphere while introducing a new and more convenient way to...

The reduction principle is a common idea which states that while researching the stability of solutions of the dynamic system (the system of differential, difference, differential-difference equations) the order of the researched system can be decreased. As the main obstacle in researching a dynamic system is a big dimension of the system, decreasing the order significantly simplifies the stability of the research process.§This work contains some ways of decreasing the system order. The author aimed to keep the details to a minimum, to facilitate a better understanding of the main ideas, and...