Abstract
The stability problem of the general class of linear systems with multiple time delays is addressed in this paper. Firstly, original polynomial eigenvalue problem (PEVP) of the time delay system (TDS) is transformed into new PEVP by proposing the linear fractional mapping (transformation). We compute the eigenvalues of the new PEVP with the help of con-tour integral based eigensolver inside an open unit disk. Finally, we substitute the computed eigenvalues of the new PEVP (inside the open unit disk) into eigenvalues of the original PEVP (in the open half complex plane) using linear fractional mapping. The mathematical framework of this numerical method is easy to implement compared to the existing methods, and we can save the high computational cost. Numerical examples are given to demonstrate that our approach is practical and stable.
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