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This paper considers the problem of stabilizing switched time-delay linear systems through a state-dependent switching strategy. In contrast to the existing works, we adopt a less restrictive assumption of the system, and show that this assumption is sufficient to guarantee asymptotic stability of the considered system under the min-projection switching strategy. Our results also imply that the min-projection switching strategy, originally designed for delay-free switched systems, is robust with respect to small state delays. An optimization problem is formulated to estimate the upper bound of the tolerable time delay. Numerical examples are presented to show that our method is applicable to a larger class of switched systems and leads to a greater delay bound.

Stabilization of Switched Time-Delay Linear Systems through a State-Dependent Switching Strategy