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 that they correspond to stable polynomials in linear discrete-time systems, have been attained. Procedures are presented in this paper to search for a suitable transform parameter β that will achieve a possibly larger coefficient perturbation range (with guaranteed stability) than that obtained by Soh et al. [7]. When β = 0, the hyperel-lipsoid degenerates to the largest hypersphere [7]. The result in this paper is, therefore, a generalization of the result obtained in [7].