SINGULAR SENSITIVITY AND ROBUST ESTIMATES OF DYNAMIC SYSTEMS

Abstract

The problem under consideration is connected with the need to ensure the stability of ellipsoidal estimates of the quality of the functioning of control systems under conditions of variations or uncertainty in the parameters of their structural elements, and, consequently, with the development of a technology for assessing their instability caused by these factors. To assess the stability of ellipsoid quality estimates of multivariable control systems, the sensitivity functions of the first order of singular values, singular bases and the condition number are used. SVD analysis of singular sensitivity matrices makes it possible to compare the course of multidivariable controlled processes and solve the applied problem of diagnosing complex dynamic systems by determining the dominant parameters, their most unfavorable combinations, evaluating the effect of introducing a controller, searching for the optimal value, and also ranking parameters, which is especially valuable in the model formation phase.