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Robust stability analysis of sampled-data systems via periodically time-varying scaling

Stimulated by a general necessary and sufficient condition for robust stability of sampled-data systems derived through the Nyquist stability criterion in an operator-theoretic framework, we introduce linear periodically time-varying (LPTV) scaling to sampled-data systems in this paper. We first give a simple example demonstrating that this new scaling can lead to exact robust stability analysis. We then study some basic properties of LPTV scaling, and show that the effectiveness of such scaling is unique to sampled-data systems (and LPTV systems) in the sense that it offers no advantage over the conventional linear time-invariant (LTI) scaling when the feedback loop consists of only LTI systems. It turns out, however, that LPTV scaling is generally more effective than the conventional LTI scaling regarding robust stability analysis when there is at least one norm-bounded static uncertainty block