Constrained exponential stabilizability of marginal and/or unstable linear systems

It has been established that the constrained asymptotic stabilization of marginal and/or unstable linear systems on the constrained asymptotically stabilizable set is possible by non-linear control and that the constrained exponential stabilization on any compact subset of the constrained asymptotically stabilizable set is possible by linear control. However, we show in this paper that the constrained exponential stabilization of such systems on the constrained asymptotically stabilizable set is impossible by any control law.