A new method for the stability robustness determination of state space models with real perturbations

The authors consider the robust stability of a linear time-invariant state-space model subject to real plant data perturbations. The problem is to find the distance of a given stable matrix from the set of unstable matrices. A novel method, based on the properties of Kronecker product and two other composite matrices, is developed to achieve this aim: The method makes it possible to distinguish real perturbations from complex ones. Explicit bounds on the distance of a stable matrix from the set of unstable matrices are obtained for both the continuous-time and discrete-time case. The bounds are applicable only for the case of real plant perturbations; hence they are less conservative to apply than for the case when complex perturbations are allowed. Several examples are given to demonstrate the new bounds, which in general are shown to be tighter than results previously reported