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
LMI
cancellation problems
delta operators
scaling procedure
linear matrix inequalities
numerical sensitivity
Author
Bengt Lennartson
Chalmers, Signals and Systems, Systems and control
R. Middleton
University of Newcastle
Ivar Gustafsson
University of Gothenburg
Chalmers, Mathematical Sciences, Mathematics
IEEE Transactions on Automatic Control
0018-9286 (ISSN) 1558-2523 (eISSN)
Vol. 57 11 2873-2879 6176205Areas of Advance
Production
Subject Categories
Computational Mathematics
Control Engineering
DOI
10.1109/TAC.2012.2192361