Numerical sensitivity of Linear Matrix Inequalities for shorter sampling periods

The numerical sensitivity of Linear Matrix Inequalities (LMIs) arising in the H_∞ norm computation in discrete time is analyzed. Rapid sampling scenarios are examined comparing both shift and delta operator formulations of the equations. The shift operator formulation is shown in general to be arbitrarily poorly conditioned as the sampling rate increases. The delta operator formulation includes both recentering (to avoid cancellation problems) and rescaling, and avoids these difficulties. However, it is also shown that rescaling of the shift operator formulation gives substantial improvements in numerical conditioning, whilst recentering is of more limited benefit.