Abstract

We study the strict feasibility of the linear matrix inequality (LMI) and its dual for H ∞ state feedback control problem for the multi-input multi-output (MIMO) servo system. Then we show that weighting functions with unstable zeros improve the numerical accuracy. We discuss the relationship between the zeros in the weighting function and the strict feasibility of the dual LMI. This is closely related to the numerical accuracy of LMI solvers because algorithms implemented in LMI solvers require the strict feasibility for both the LMI and its dual. Furthermore, we provide closed-form expression of the performance limitation when given plants have one or two unstable invariant zeros. The non-strict feasibility of the dual plays an essential role in the expression.

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