access icon free 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.

Inspec keywords: FIR filters; discrete time systems; robust control; linear matrix inequalities

Other keywords: linear matrix inequality condition; robust stability analysis; FIR separator; structured uncertainty; separator type robust stability condition; static scaling; dynamic scaling; FIR scaling; separator type condition; discrete time linear time invariant system; finite impulse response scaling

Subjects: Linear algebra (numerical analysis); Stability in control theory; Signal processing theory; Discrete control systems

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