DETERMINING THE DEGREE OF SYSTEM VARIABILITY FOR TIME-VARYING DISCRETE-TIME SYSTEMS

The paper develops the concept of a variability coefficient for linear time-varying (LTV), discrete-time (DT) systems. The main idea is to introduce frequency analysis tools for LTV systems which involve Singular Value Decomposition (SVD) and Discrete Fourier Transform (DFT) as well as Power Spectral Density (PSD). The general objective of this paper is to examine the first order system to show how the value of the proposed variability coefficient depends on the variability of particular system parameters and whether it is a good measure of the degree of the system variability. Especially we examine how the variability of two matrices of the state space model (scalars, in this case 1st order) influences the value of this coefficient. Three different cases of one-dimensional LTV DT system have been considered. The results of analysis for each case are shown in 2 diagrams: five proposed coefficients versus given parameter epsilon and step responses for given parameters. Examples are preceded by theoretical considerations and on the basis of these examples the most important conclusions are drawn and properties of the introduced concept summarized.