An upper bound of the reachability index for a special class of positive 2-D systems

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.