Criteria for the stability of linear systems and mathematical models for their analysis

The stability criteria defined in the standard theory of linear systems are not exhaustive and demonstrate some inconsistencies. This scientific article discusses the problem of stability of linear systems and the mathematical models used to analyze it. The concept of stability and criteria determining the stability of linear systems are also considered. The main attention is paid to the definition of new stability criteria that are more consistent with real physical situations. In particular, a distinction is made between static stability and dynamic stability in order to analyze the stability of systems in the time domain and in the equivalent image domain, taking into account the Laplace transform.