Qualitative Exponential Stability and Instability of Dynamical Systems and Range Estimation of Parameter Acceptable Changes

摘要

The main purpose of the research is the extending of the concept of qualitative exponential stability and instability for a wider class of the dynamical systems and objects as well as developing of analytic and calculating technologies for analyzing the quality of processes and projecting of control devices for control systems. And if the property of asymptotic stability indicates the convergence or divergence of the processes in time, the exponential stability provides information about the speed of convergence or divergence processes, thereby characterizing the rapidness of the system. Meeting the conditions of quality exponential stability evaluates the average rate of convergence or divergence of processes, as well as ongoing processes of deviations of the time-average behavior, the last gives information about the behavior of transients (oscillation, overshoot). Development of analytical and computational techniques for the analysis of stability and instability of comparison systems and, as a result of multiply-connected systems, as well as the processes quality is almost an essential task for the study.