Some remarks on the robustness of adaptive pole assignment

The properties of a closed-loop system, subject to bounded disturbances, are analyzed when a pole placement control law is implemented on the basis of a model that cannot be falsified by the resulting input/output data. Such models are the best that can be obtained from any identification method driven by the prediction error in the closed-loop and given the uncertainty on the disturbance. In the absence of disturbances such a model would give to rise to closed-loop behavior as if the poles are assigned. However, if the presence of arbitrary small disturbances is assumed, such a result does not even hold approximately and only stability can be guaranteed; pole placement cannot be achieved. As a consequence, the system behavior is not continuous in the magnitude of the upper bound of the disturbance