New stability criteria for linear time-delay systems

Several new stability criteria for linear time-delay systems are presented by the corresponding simple connected regions. From these regions, the stability of the system can be checked easily by inspecting the locations of the eigenvalues of the system matrix A₀ or its delay matrix A_d. In other words, solving any complicated characteristic equation, which contains the term exp(-hs), of the system or examining the locations of the characteristic roots by trial and error are not needed.