Brief paper: Extraction of 3D stability switching hypersurfaces of a time delay system with multiple fixed delays

Authors:
Rifat Sipahi;Ismail Ilker Delice
Affiliations:
Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA 02115, United States;Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA 02115, United States
Venue:
Automatica (Journal of IFAC)
Year:
2009

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Abstract

Stability switching hypersurfaces (SSH) of a general class of linear time invariant (LTI) multiple time delay systems (MTDS) are extracted. The number of delays @? and system order n"0 in this problem are given but they are arbitrarily large. Hence, the extraction of SSH becomes non-trivial. A novel and efficient procedure reveals the 3D projections of @?-dimensional SSH, without the need for finding the SSH. In achieving this, computation times required remain in the same order of magnitude independently of @? and n"0. Case studies demonstrate the effectiveness of the approach.