Formulas for the general solution of weakly delayed planar linear discrete systems with constant coefficients and their analysis

摘要

The paper is concerned with weakly delayed linear discrete homogeneous planar systems with constant coefficients. By the method of -transform, formulas for the general solutions, dependent on the Jordan forms of the matrix of non-delayed linear terms, are derived and the influence is analyzed of the delay on the form of the general solutions. It is shown that, after several steps, the general solutions depend only on two arbitrary parameters which are linear combinations of the initial values. This property is used to prove results on conditional stability. Linear discrete homogeneous planar systems without delay are found to have the same general solutions as the initial one. The results are illustrated by examples. Previous results are analyzed, commented and improved.