Applications of stability criteria to time delay systems

D. Popescu, University of Craiova, Craiova, Romania
V. Rasvan, University of Craiova, Craiova, Romania
R. Stefan, University "Politehnica", Bucharest, Romania

E. J. Qualitative Theory of Diff. Equ., Proc. 7'th Coll. Qualitative Theory of Diff. Equ., No. 18. (2004), pp. 1-20.

Communicated by L. Hatvani. Received on 2003-10-21
Appeared on 2004-08-31

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 of \v{C}ebotarev and Meiman (1949) up to the more recent monographs by Stepan (1989) and G\'{o}recki {\em et al} (1989) 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 of \v{C}ebotarev and Meiman and its significance within the framework of the most recent analysis of G\'{o}recki{\em et al}. The present paper aims to a fairly complete analysis of the problem combined with some hints for the nonlinear case (Aizerman problem).

State feedback stabilization based on Artstein reduction of a system with input delay to a system without delay is also considered.

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