A Controller Parametrization and Pole-Placement Design for Simultaneous Stabilization

This paper investigates the use of stable inverses to obtain multi-model controllers for the simultaneous stabilisation of a class of plants. A parametrization in terms of a stable inverse and a stable null space is proposed for all simultaneously stabilising controllers. Then a strictly proper controller design method for a particular simultaneous pole-placement is devised and the controller for this pole-placement is shown to have a multi-model structure similar to observers. For a more general pole-placement problem, it is shown that the parametrisation can be used to reduce the order of the controller to be the same as a controller designed based on generalised observers.