Improved stability robustness of linear discrete-time systems via a linear fractional transformation

Through a linear fractional transformation in the frequency domain, a set of hyperellipsoids, containing only such points in the coefficient space which correspond to stable polynomials in linear discrete-time systems, was obtained. Procedures for searching for a suitable transform parameter β that will achieve a possibly larger coefficient perturbation range (with guaranteed stability) than that obtained by C.B. Soh et al. (1985) are presented. When β=0, the hyperellipsoid degenerates to the largest hypersphere. The result in this work is, therefore, a generalization of the result obtained by C.B. Soh et al