On the Geometry of Inner Approximations to the Set of Null Controllability for Constrained Linear Systems

The problem of obtaining inner approximations to the set $$\mathcal{N}$$ of null controllability for linear systems is considered, and the geometry of certain sets arising in the approximation of $$\mathcal{N}$$ using linear feedback is explored. A two-dimensional example is worked in detail in order to delineate the limitations to the use of linear feedback.