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The stabilization of linear continuous-time systems with time delay in the state and subject to saturating controls is addressed. Sufficient conditions obtained via a linear matrix inequality (LMI) formulation are stated to guarantee both the local stabilization and the satisfaction of some performance requirements. The method of synthesis consists in determining simultaneously a state feedback control law and an associated domain of safe admissible states for which the stability of the closed-loop system is guaranteed when control saturations effectively occur.
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Tarbouriech et al. (2000) studied this question.
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