Calculation of the largest generalized stability hypersphere in the robust stability problem for the maximum setting-time and minimum damping-ratio cases

The results of a procedure which employs a geometric approach to derive the maximal ellipsoidal domains of stability in the physical parameter space, for the case in which the characteristic polynomial coefficients depend linearly on the physical parameters of the plant obtained by Biernacki et al. (see ibid., vol.AC-32, no.6, p.495-505, 1987) are extended to a more generalized stability region, such as the maximum setting time and the minimum damping-ratio cases. The method can be used to estimate the largest generalized stable hypersphere in the parameter space for a given controller