A qualitative bound in robustness of stabilization by state feedback

It is proved that placing the poles of a linear time-invariant system arbitrarily far to the left of the imaginary axis is not possible if small perturbations in the model coefficients are taken into account. Given a nominal controllable system (A/sub 0/, B/sub 0/) with one input and at least two states and an open ball around B/sub 0/ (no matter how small), there exists a real number gamma and a perturbation B within that ball such that for any feedback matrix K placing the eigenvalues of A/sub 0/+B/sub 0/K to the left of Res= gamma , there is an eigenvalue of A/sub 0/+BK with real part not less than gamma .<
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