Exponential Stability Regions Estimation of Nonlinear Dynamical Systems

Abstract

The main purpose of the research is the extending of the concept of qualitative exponential stability and instability for a wider class of dynamical systems and plants with estimating of regions of exponential stability 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 mul tiply-connected systems, as well as the processes quality is almost an essential task for the study multi-agent control algorithms and biologically inspired control algorithms in nonlinear systems, because the same systems should be related to each other and has a predetermined degree of exponential stability for the required control. Proposed results can be using in the developing flying and terrestrial robots based on biological control algorithm of living organism such as insects or bees.