Analysis of time-delay systems: Stability and instability

Several stability and instatility criteria are provided for linear time-delay systems. A part of the results is a generalization of the formerly reported stability theorems and other part forms an instability counterpart of them. Stability or instability property of the systems is checked by examining whether the eigenvalue-loci of some matrix involving system parameters lie in certain region of the complex plane. This task can be successfully carried out with the aid of personal computers with graphic display terminals. Some examples are worked out to demonstrate the present approach.