A unified Krylov-Bogoliubov-Mitropolskii method for solving \(n\)th order nonlinear systems. (English) Zbl 1019.93022
Summary: A unified theory is presented for obtaining the transient response of \(n\)th order nonlinear systems with small nonlinearities by the Krylov-Bogoliubov-Mitropolskii method. The method is a generalization of Bogoliubov’s asymptotic method and covers all three cases when the roots of the corresponding linear equation are real, complex conjugate, or purely imaginary. It is shown that by suitable substitution for the roots in the general result that the solution corresponding to each of the three cases can be obtained. The method is illustrated by examples.
MSC:
| 93C10 | Nonlinear systems in control theory |
| 93B51 | Design techniques (robust design, computer-aided design, etc.) |
References:
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