Representation of solutions of discrete delayed system x(k+1)=Ax(k)+Bx(k−m)+f(k) with commutative matrices

By Josef Diblík, D. Khusainov. 2006

107 citations recorded by the source corpus.

Abstract In the investigation performed we give, on half-infinity discrete intervals, formulas for solution of initial problem of linear discrete systems x ( k + 1 ) = A x ( k ) + B x ( k − m ) + f ( k ) with constant square matrices A, B such that A B = B A , det A ≠ 0 and with a vector function f ( k ) . Corresponding representations are obtained with the aid of so-called discrete matrix delayed exponential, which permits to represent solutions in a matrix form similarly as for ordinary differential systems with constant matrices, or as well as for differential systems with constant matrices and constant delay.

Subfields: Computational Theory and Mathematics, Mechanical Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/5011e2b25dbd3409d6d317eaf8db4f8a5fc778ec

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Blanka Morávková
2. Josef Diblík

In Mechanical Engineering

1. Blanka Morávková
2. Josef Diblík

In Numerical Analysis

1. Blanka Morávková
2. Josef Diblík

Citations in the corpus

• Representation of the Solutions of Linear Discrete Systems with Constant Coefficients and Two Delays (2014, background): “2 Abstract and Applied Analysis In [1, 2], a discrete matrix delayed exponential for a single delaym ∈ N was defined.”