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

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 ℓ 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 ℓ -dimensional SSH, without the need for finding the SSH. In achieving this, computation times required remain in the same order of magnitude independently of ℓ and n 0 . Case studies demonstrate the effectiveness of the approach.