Reachable, controllable sets and stabilizing control of constrained linear systems

We consider discrete-time linear systems with constrained controls. We present an algorithm for computing an external representation of the N-step reachable set and controllable set. It is an improvement of previous methods. In particular, it is shown that for constructing the set of initial states that can be driven to the origin asymptotically, one can restrict the search to a polyhedral set in the unstable subspace of the autonomous system, which yields a drastic reduction in the computational burden. Application to the synthesis of stabilizing feedback controllers is discussed.

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