Representation of the Solutions of Linear Discrete Systems with Constant Coefficients and Two Delays

Abstract EN

The purpose of this paper is to develop a method for the construction of solutions to initial problems of linear discrete systems with constant coefficients and with two delays Δ x ( k ) = B x ( k - m ) + C x ( k - n ) + f ( k ), where m , n ∈ ℕ , m ≠ n, are fixed, k = 0 , … , ∞ , B = ( b i j ) , C = ( c i j ) are constant r × r matrices, f is a given r × 1 vector, and x is an r × 1 unknown vector.

Solutions are expressed with the aid of a special function called the discrete matrix delayed exponential for two delays.

Such approach results in a possibility to express an initial Cauchy problem in a closed form.

Examples are shown illustrating the results obtained.