Graph-theoretic approach for structural controllability of two-dimensional linear systems

Abstract

Abstract The aim of this work is to present some criteria of structural-controllability relative to a certain structural two-dimensional linear systems. The most important property of two-dimensional systems is that the information is spread in two independent directions. To study their structural-controllability, we considered a new structural digraph associated with the different structural two-dimensional linear systems. The construction of this structural digraph is based on the disjoint-union graph notion, which translates the independence of the two dynamics, and consider separately the horizontal and vertical part of the state space model representation of two-dimensional systems. We define the two-dimensional disjoint-union digraph of structural Givone–Roesser model, and determine the two-dimensional disjoint-union digraph of structural Fornasini–Marchesini model, finally we derive a criteria based on the two-dimensional disjoint-union digraph.