Robust stability analysis based on finite impulse response scaling for discrete-time linear time-invariant systems

In this study, we discuss a dynamic scaling approach exploiting the separator-type robust stability condition for discrete-time linear time-invariant systems. We confine ourselves to a class of what we call finite impulse response (FIR) separators, and establish a systematic and practical framework of searching for an FIR separator satisfying the separator-type condition. The first step is to give explicit structure of FIR separators suitable for dealing with a given set of structured uncertainties. The second step is to give an explicit linear matrix inequality condition for the analysis. In particular, a minimal realisation of an augmented system to be dealt with in FIR scaling is derived, which is non-trivial and is very important in reducing the computational load in the numerical computation. Effectiveness of the developed framework is demonstrated numerically, through comparison with the conventional static scaling and μ-analysis.