Special approach to the stability criteria for linear systems

This study introduces two new criteria for the stability of linear systems, based on the researches carried out in the field of stability criteria in the frequency domain. They are based on the implementation of the Pontarayn´s criterion in systems with delay, as well as on the Cauchy´s theorem of arguments in the domain of positive change in the arguments of the function f*(jω, ej^τω), regarding stable systems and the zeroes of characteristic equation located in the left semi-plane of the s-plane. On the given example of a linear system through the characteristic equation of the forth order, the analysis of stability features is clearly depicted, for all possible cases of the system, along with the obvious correspondence with the results of Hurwic and Mihailov, that is, their criteria.