Applications of stability criteria to time delay systems
Dan PopescuElectronic Journal of Qualitative Theory of Differential Equations
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Abstract
Stability and stabilization of time delay systems (even of the linear ones) is again in the mainstream of the research. A most recent example is the stability analysis of feedback control loops containing a first order controlled object with pure delay and a standard PID controller, thus generating a system with a second degree quasi-polynomial as characteristic equation. Since the classical memoir ofČebotarev and Meiman (1949) up to the more recent monographs by Stepan (1989) and several approaches to this problem have been given, aiming to find the most complete Routh-Hurwitz type conditions for this case. In fact the main problem is here a missing case in the original memoir ofČebotarev and Meiman and its significance within the framework of the most recent analysis of Górecki et al. The present paper aims to a fairly complete analysis of the problem combined with some hints for the nonlinear case (Aizerman problem).
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