The structural property of local reachability for positive two-dimensional (2-D) systems refers to single local states. The smallest number of steps needed to reach all local states of a system is the local reachability index of the system. This index may exceed the system dimension. Some authors have studied upper bounds on the local reachability index for specific positive 2-D systems and have suggested different upper bounds for any positive 2-D system. In this brief, the local reachability index for a special class of positive 2-D systems is characterized, and an upper bound for this index is derived. A comparison with previous results is also presented.Index Terms-Hurwitz products, influence digraph, local reachability index, nonnegative matrices, positive two-dimensional (2-D) systems, reachability.
Abstract. The smallest number of steps needed to reach all nonnegative local states of a positive two-dimensional (2-D) system is the local reachability index of the system. The study of such a number is still an open problem which seems to be a hard task. In this paper, an expression depending on the dimension n as well as an upper bound on the local reachability index of a special class of systems are derived. Moreover, this reachability index is greater than any other bound proposed in previous literature.
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