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

Stability switching hypersurfaces (SSH) of a general class of linear time invariant (LTI) multiple time delay systems (MTDS) are extracted. The number of delays ℓℓ and system order n0n0 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 ℓℓ-dimensional SSH, without the need for finding the SSH. In achieving this, computation times required remain in the same order of magnitude independently of ℓℓ and n0n0. Case studies demonstrate the effectiveness of the approach.