Abstract
The instability of nonlinear nonautonomous dynamic systems of arbitrary order is studied. A special class of parameter-dependent scalar functions is used in Part I, which describes the preliminaries, to derive new necessary and sufficient conditions for the instability of equilibrium states of such systems. In Part II, these special functions are used to express new sufficient conditions of instability for a particular class of unstable nonlinear dynamic systems in terms of functions having a simple geometric meaning.
Similar content being viewed by others
REFERENCES
Zhukov, V.P., Necessary and Sufficient Conditions for the Asymptotic Stability of Nonlinear Dynamic Systems, Avtom.Telemekh., 1994, no. 3, pp. 24-36.
Zhukov, V.P., Necessary and Sufficient Conditions for the Asymptotic Stability of Nonlinear Nonautonomous Dynamic Systems, Avtom.Telemekh., 1995, no. 9, pp. 29-48.
Zhukov, V.P., An Investigation into the Asymptotic Stability of Nonlinear Nonautonomous Dynamic Systems with the Uniformity Requirement, Avtom.Telemekh., 1998, no. 4, pp. 25-40.
Krasovskii, N.N., Nekotorye zadachi teorii ustoichivosti dvizheniya (Certain Problem in the Theory of Stability of Motion), Moscow: Fizmatgiz, 1959.
Hartman, P., Ordinary Differential Equations, New York: Wiley, 1964. Translated under the title Obyknovennye differentsial'nye uravneniya, Moscow: Mir, 1970.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zhukov, V.P. Instability Conditions for Nonlinear Nonautonomous Dynamic Systems. I. Automation and Remote Control 63, 1724–1729 (2002). https://doi.org/10.1023/A:1020995013004
Issue Date:
DOI: https://doi.org/10.1023/A:1020995013004