Abstract
A simple and quick method is proposed for estimating the asymptotic stability of highly nonlinear dynamic systems, in particular, high-dimensional systems for which Taylor series of the right sides of differential equations converge slowly and the sum of terms whose order of smallness is more than two can considerably exceed the value of any second-order term. In this case, the method of Lyapunov functions cannot guarantee a correct stability estimate. The new method is based on a procedure of maximizing the rate of the change in the metric of the perturbed state space. This metric can turn out to simultaneously be a Lyapunov function only in particular cases. The proposed new method is not aimed at estimating the stability of linear systems.
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*This work was supported by the RFBR (Russian Foundation for Basic Research) Program, project No. 18-01-00842-a.
Translated from Kibernetika i Sistemnyi Analiz, No. 4, July–August, 2019, pp. 15–23.
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Smol’yakov, E.R. An Efficient Method for Stability Analysis of Highly Nonlinear Dynamic Systems*. Cybern Syst Anal 55, 531–538 (2019). https://doi.org/10.1007/s10559-019-00161-4
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DOI: https://doi.org/10.1007/s10559-019-00161-4