Stability Analysis of Linear Time-Delay Systems with Two Incommensurate Delays

Abstract

The contribution focuses on the stability analysis of linear time-delay systems within the framework of the Lyapunov – Krasovskii functionals. The method used is based on the idea to check positive definiteness of the functionals exclusively on the specific Razumikhin-type set of functions. For the systems with incommensurate delays, it is proposed to use the modified functionals depend on the Lyapunov delay matrix related to a nominal system with commensurate delays. The method is applied for the estimation of the stability domains in the parameter space.