Numerical sensitivity of Linear Matrix Inequalities for shorter sampling periods
Paper i proceeding, 2012

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.


Bengt Lennartson

Chalmers, Signaler och system, System- och reglerteknik, Automation

R. Middleton

University of Newcastle, Australia

Proceedings of the IEEE Conference on Decision and Control

01912216 (ISSN)

Article number 6425801 4247-4252 6425801



Elektroteknik och elektronik