Computing quasi-LTI robustness margins in sampled-data systems

The robustness test for sampled-data systems with slowly time-varying perturbations is known to be infinite dimensional in nature. This note develops computationally explicit upper and lower bounds for the corresponding stability radius, presenting them in terms of linear matrix inequalities (LMIs) given by state-space formulas derived. The upper bound is shown to converge monotonically to the stability radius, and so can be systematically tightened at the cost of increased computational effort. The lower bound is monotonically increasing, and is conjectured to also converge to the stability radius.