Stabilization of linear unstable systems with control constraints

We consider linear systems with possibly exponentially unstable eigenvalues and with saturating input. It is shown that for a class of unstable systems there exists a bounded linear stabilizing controller for sets of initial conditions which may be arbitrary large and bounded in some directions of the state space while other directions must be bounded. Hence the results are stronger than the existing local stability results and weaker than semi-global stability (impossible to obtain for unstable systems). Moreover, sufficient conditions for the existence of stabilizing controllers when the system is subject to plant disturbances and measurement noise are also given