The paper is devoted to a generalization of the Myshkis's 3/2 stability theorem. This theorem gives an exact stability boundary for a scalar equation with a real parameter and an arbitrary delay, which is bounded by a prescribed value. In our paper, we consider the equation with complex parameter that opens up a direct opportunity for the analysis of systems of several equations. Via the Razumikhin approach, a stability region (not necessarily exact) is obtained, it is shown that its boundary can be expressed in radicals, and in the limit case the result coincides with the one of Myshkis.

Original languageEnglish
Pages (from-to)85-90
Number of pages6
JournalIFAC-PapersOnLine
Volume52
Issue number18
DOIs
StatePublished - Sep 2019
Event15th IFAC Workshop on Time Delay Systems (TDS) jointly held with the 7th IFAC Symposium on System Structure and Control (SSSC) - Sinaia, Romania
Duration: 9 Sep 201911 Sep 2019

    Research areas

  • linear systems, Myshkis theorem, Razumikhin approach, stability analysis, time delay, time-varying systems

    Scopus subject areas

  • Control and Systems Engineering

ID: 53452034