Summary
For quadratic state vectors or suitable other norms of time-variant systems we introduce stochastic transformations to get time-invariant drift terms in the transformed state equations. This mapping defines a deterministic eigenvalue problem which can be solved by means of functional analytic methods for the investigation of moments behaviour, mean square stability or related Lyapunov exponents.
The identification of a given power spectrum is performed in the time domain of the associated correlation functions by minimizing the quadratic forms of correlation operators. Stability and physical existence of the identified dynamic systems are ensured. The identification is extended to the response spectra of nonlinear dynamic systems under white noise.
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© 1988 Springer-Verlag Berlin Heidelberg
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Wedig, W. (1988). Mean Square Stability and Spectrum Identification of Nonlinear Stochastic Systems. In: Ziegler, F., Schuëller, G.I. (eds) Nonlinear Stochastic Dynamic Engineering Systems. IUTAM Symposium. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83334-2_10
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DOI: https://doi.org/10.1007/978-3-642-83334-2_10
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