The pole placement theorem and small perturbations in parameters: the existence of an unassignable left half plane

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. The results show a major difference between the behavior of nominal closed-loop system poles and the closed-loop system poles under small perturbations of the open-loop system parameters. For systems with uncertain parameters there exists an unassignable left half plane.<>