Abstract

In this paper, we first study the stabilization of an LTI anti-stable planar system with a saturated linear state feedback. We show that the domain of attraction of such a system under any saturated linear stabilizing feedback can be obtained easily by simulating the time-reversed closed-loop system. We then show that a saturated linear state feedback can be designed for such a system so that the equilibrium of the closed-loop system has a domain of attraction that is arbitrarily close to the null controllable region. Finally we present an extension of this result to general LTI systems with planar anti-stable dynamics.

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