Stability analysis of perturbed systems for investigation of limited boundedness of their solutions

Stability theory play an important role in systems theory and engineering sciences. The stability of equilibrium points is usually considered within the framework of the theory of stability developed by the Russian mathematician and mechanic A. M. Lyapunov (1857–1918), who laid its foundations and gave it a name. At present, it has become very routine view at stability as stability with respect to a perturbation of the input signal. The research is based on the space-state approach for modeling nonlinear dynamic systems and the alternative input-output approach. The concept of stability in terms of input-output of a nonlinear system is based on the method of Lyapunov functions and its generalization to the case of nonlinear dynamic systems. The interpretation of the problem of the accumulation of perturbations is reduced to the problem of finding the norm of the operator, which makes it possible to expand the range of models under research depending on the space in which the input and output signals act.