Numerical Sensitivity of Linear Matrix Inequalities Using Shift and Delta Operators
Journal article, 2012

The numerical sensitivity of linear matrix inequalities (LMIs) arising from discrete-time control with short sampling periods is analyzed using shift and delta operators. The delta operator avoids cancellation problems for short sampling periods, and it includes a system scaling proportional to the inverse of the sampling period. The numerical sensitivity of both these mechanisms is investigated analytically, and verified by numerical examples. The conclusion is that the scaling procedure is (somewhat surprisingly) much more essential for shorter sampling periods than avoiding the cancellation problem.

shift operators

sampling periods

discrete-time control

system scaling


cancellation problems

delta operators

scaling procedure

linear matrix inequalities

numerical sensitivity


Bengt Lennartson

Chalmers, Signals and Systems, Systems and control, Automation

R. Middleton

University of Newcastle, Australia

Ivar Gustafsson

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

IEEE Transactions on Automatic Control

0018-9286 (ISSN)

Vol. 57 11 2873-2879 6176205

Areas of Advance


Subject Categories

Computational Mathematics

Control Engineering



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