Determination of Positive Realization of Two Dmensional Systems Using Digraph Theory and GPU Computing Method

Abstract

In the recent years many researchers were interested in positive two-dimensional (2D) linear systems. Analysis of positive 2D systems is more difficult than of positive onedimensional (1D) systems. A lot of numerical problems that arised in positive 2D systems are unsolved completely, for examples: minimal positive realization problem, determination of lower and upper index reachability, determination of reachability index set, determination of state matrices from characteristic polynomial, etc. In many case this problems cannot be solved analytically by hand. To solve this problems we can use new computational method based on digraph theory and CPU or GPU computing method. A new method of determination positive realization of two-dimensional systems using digraph theory will be proposed. A procedure for computation of the state matrices will be given. The procedure will be illustrated by a numerical example.