A recent stability analysis, the Direct Method, for linear time invariant, time delayed systems (LTI-TDS) is revisited in this work considering the degenerate system dynamics. The principal strengths and enabling novelties of the method are reviewed along with its structured steps involved for assessing the stability. Uncommon in the literature, the Direct Method can handle large dimensional systems (e.g., larger than two) very comfortably. It returns an explicit formula for the exact stability posture of the system for a given time delay, as such it reveals the possible detached stability pockets throughout the time delay axis. Both retarded and neutral classes of LTI-TDS are considered in this work. The main contribution here is to demonstrate the ability of the Direct Method in tackling degenerate cases. Along with the analytical arguments, example case studies are provided for a group of degeneracies. It is shown that the new method is capable of resolving them without any difficulty.
Degenerate Cases in Using the Direct Method
Contributed by the Dynamic Systems and Control Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the ASME Dynamic Systems and Control Division, June 2002; final revision, December 2003. Associate Editor: G. Ulsoy.
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Sipahi , R., and Olgac, N. (June 4, 2003). "Degenerate Cases in Using the Direct Method ." ASME. J. Dyn. Sys., Meas., Control. June 2003; 125(2): 194–201. https://doi.org/10.1115/1.1567756
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