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Numerical Sensitivity of Linear Matrix Inequalities Using Shift and Delta Operators

Bengt Lennartson, Chalmers

Abstract:

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 much more essential for shorter sampling periods than avoiding the more well known cancellation problem.

Presentation Slides