Control of time delay processes with uncertain delays: Time delay stability margins

In this paper, the stability of time delay processes that have uncertain delays is considered, and the maximum allowable perturbation which may occur in the time delays so as to maintain stability are determined. In particular, the characteristic equations of time delay systems are quasipolynomials, whose roots determine the stability of such systems, and the root-locus of these equations in specified desired regions is investigated. A numerical algorithm is presented for the calculation of the time delay stability margins in the space of time delays for such systems, and the size of the stability hyperspheres in this space is computed. To illustrate the procedure, the algorithm is applied to process control systems with uncertain delays and the allowable perturbations in the time delays of these systems are then computed.