Determination reachability index space of positive two-dimensional linear system using digraph-based theory

In this paper, a the new alternative method for determination of a reachability index space has been proposed. The method is based on the digraphs theory. As a solution of the problem of determination of a lower reachability index, the method finds all possible finite paths in the digraphs. By performing complete traversal of the digraphs we are able to reach all the possible lower reachability indices for any number of variables at once. Having determined the lower and upper reachability index, we can determine a reachability index space in an easy way. The proposed method is illustrated with numerical examples.