Abstract
For the nonlinear dynamic systems of arbitrary order, consideration was given to stability of the equilibrium states in the limit-critical case where the linear system obtained by linearization of a nonlinear system is such that all roots of its characteristic equation have zero real parts. In this—as in any other—critical case, the nature of stability of the nonlinear system is defined by the nonlinear terms of its right-hand side. Therefore, for the nonlinear system at hand it is desirable to have conditions for (asymptotic, nonasymptotic) stability and instability formulated only in terms of the nonlinear terms. The present paper obtained these desirable sufficient conditions for stability and instability on the basis of some properties that are characteristic of the solutions of the linearized system in the limit case under study.
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Zhukov, V.P. On Conditions for Stability of the Nonlinear Dynamic Systems in the Limit-Critical Case. Automation and Remote Control 64, 1690–1701 (2003). https://doi.org/10.1023/A:1027318010990
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DOI: https://doi.org/10.1023/A:1027318010990