Abstract
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.
Highlights
Modern hardware of computers and computer technology analysis of the behavior of multiply dynamic systems provides efficient algorithms for comparison of systems based on the Lyapunov functions, which are the result of the synthesis of multiply-connected systems
The ideology worked out permit to consider qualitative exponential stability and instability for systems and objects with continuous and discrete time and determine the sufficient local conditions to ensure these types of stability
Let these areas are connected and include the origin of coordinates
Summary
Modern hardware of computers and computer technology analysis of the behavior of multiply dynamic systems provides efficient algorithms for comparison of systems based on the Lyapunov functions, which are the result of the synthesis of multiply-connected systems. The modular Lyapunov functions greatly simplify the procedures for the investigation of such system’s behavior. The terms of exponential and qualitative exponential stability and instability, obtained on the basis of modular Lyapunov functions, can judge the behavior of processes and their quality of multiply-connected systems., Algorithms and software, developed on the basis of the results, obtained in [1,9], allow to solve the problems of analysis and synthesis of continuous and discrete multiply-connected systems with linear objects. The ideology worked out permit to consider qualitative exponential stability and instability for systems and objects with continuous and discrete time and determine the sufficient local conditions to ensure these types of stability
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