A SAMPLE TIME ASSIGN FOR A DISCRETE INTERVAL PARABOLIC SYSTEM WITH THE TWO-DIMENSIONAL UNCERTAIN PARAMETER SPACE

摘要

In the paper, the sample time assign problem for a class of uncertain parameter discrete parabolic systems is presented. The system under consideration is described by the discrete abstract state space equation in the Hilbert space. The system's uncertainty is described by the two-dimensional vector containing uncertain parameters of a heat equation. The type of the system uncertainty implies that the state operator and the control operator for the discussed system are interval operators. As a measure of the system's uncertainty the weighted mean of widths of interval state equation coefficients and the Euclidean norm of the both widths were accepted. The proposed performance indices allow us to calculate a range of sample time that guarantees that the required maximal permissible system's uncertainty will not be exceeded after a system's discretization. The results are depicted by means of an example.