Linear systems with finite signal-to-noise ratios: a robustness approach

A recently introduced representation of the inevitable uncertainty in models of controlled systems is the so-called finite signal-to-noise ratio (FSN) model where disturbances are modeled as white noise the intensity of which depend affinely on the variance of some signals in the controlled system. In this paper we show that analysis and synthesis of FSN systems can be seen as a robustness problem by interpreting the FSN disturbances as outputs of unknown system components, termed noise generators. This robustness problem is analogue to the μ problem. We define a new measure μ₂ which quantifies robustness towards noise generators and present an explicit expression for evaluating this measure as well as a D-K-iteration type algorithm for design