Development of a Graph Model and Algorithm to Analyze the Dynamics of a Linear System with Delay

Abstract

The article deals with the problem of modeling and calculating processes in a linear system with a delay based on dynamic graphs. A graph model of a continuous lagging signal (initial function) is constructed. A graph model of a linear stationary system with a delay in the feedback chain is constructed as a union of graph models of its elements. The graph model makes it obvious that a system with a delay in the feedback circuit is open relative to the signals flowing in it, which makes it possible to significantly simplify computational procedures. A linear system with a delayed control signal is also considered. Based on graph models the authors obtain the recurrent relations and an algorithm for calculating processes in a linear system with a delay in state and a delay in control. The paper presents an example of using the obtained algorithm. The proposed method allows for a clear and strict formalization of the description and analysis of complex systems, including nonlinear discrete systems with different types of modulation