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

Abstract

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 separatortype 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.

Piecewise observers of rectangular discrete fuzzy descriptor systems with multiple time-varying delays

“…A great number of references have been reported on discrete-time systems. For example, the stability and robust stability for discrete-time linear systems has been investigated in paper [22,14,15]. Moreover, a discrete-time queueing model has been developed in paper [32], and performance of the model has been studied under realistic conditions.…”

“…where (i, j) ∈ Φ. According to the denotation of coefficient matrices in system (7) and observer (9), we can, from inequality (14), obtain that…”