Robust stability of discrete-time systems under parametric perturbations

Stability robustness analysis of a system under parametric perturbations is concerned with characterizing a region in the parameter space in which the system remains stable. In this paper, two methods are presented to estimate the stability robustness region of a linear, time-invariant, discrete-time system under multiparameter additive perturbations. An inherent difficulty, which originates from the nonlinear appearance of the perturbation parameters in the inequalities defining the robustness region, is resolved by transforming the problem to stability of a higher order continuous-time system. This allows for application of the available results on stability robustness of continuous-time systems to discrete-time systems. The results are also applied to stability analysis of discrete-time interconnected systems, where the interconnections are treated as perturbations on decoupled stable subsystems.