Reachability of Linear Systems over the Symmetrized Max-Plus Algebra

Abstract

The criteria of reachability [resp. observability] of max-plus algebraic linear system is determined using asticity of columns or rows of reachability [resp. observability] matrix. In this paper, we determine the criteria of reachability [resp. observability] of symmetrized max-plus algebraic linear system. The determination of these criteria is carried out using rank of reachability [resp. observability] matrix. The linear system is reachable [resp. observable] when the reachability [resp. observability] matrix is full row or column rank in balance sense.

Keywords: Linear Systems; Observability; Reachability; Rank; Symmetrized Max-Plus Algebra.

2010 Mathematics Subject Classification. 93C05; 15A03; 15A80