Graph Models and Algorithm for Studying the Dynamics of a Linear Stationary System with Variable Delay

Abstract

In this article, we consider the problem of studying the dynamics of linear objects with variable delay based on graph models. The output signal of the variable lag element is deformed along the time axis. The function that is the output of the rung will be either "compressed" or "stretched" on the time axis relative to the input function. Conditions for the physical realizability of an element with a variable delay are given. The physical properties of the variable delay element and the generality of individual stages in the formation of models of systems with constant and variable delay are taken into account. A linear variable delay system can be studied using matrix equations. On the basis of the graph model, relations are obtained for calculating processes in a linear system with variable delay. The graph model of the system makes it possible to bypass laborious calculations and to exclude operations associated with insufficient matrix density. The above scheme can also be used to calculate processes in variable delay systems in the control channel.