Spectral balance: A frequency domain framework for analysis of nonlinear dynamical systems

Andrzej Banaszuk, Prashant G. Mehta, Igor Mezić

Research output: Contribution to journalConference articlepeer-review


A frequency-domain framework for analysis, computations, and uncertainty propagation in nonlinear systems driven by broad-band disturbances is introduced and illustrated in a simple example of a nonlinear system that exhibits noise-induced transitions between two stable equilibria. The spectral balance framework generalizes the standard harmonic and Gaussian signal balance in feedback systems. The application example presented is a scalar model with cubic nonlinearity after pitchfork bifurcation driven by a broad-band disturbance. An approximate and iterative spectral balance (including determination of equilibria) is solved. The solution of the approximate spectral balance is used to reformulate the original model using a loop transformation so that an iterative procedure for finding the spectrum of the output converges to the true spectrum of the solution.

Original languageEnglish (US)
Article numberWeB12.4
Pages (from-to)2244-2249
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
StatePublished - 2004
Externally publishedYes
Event2004 43rd IEEE Conference on Decision and Control (CDC) - Nassau, Bahamas
Duration: Dec 14 2004Dec 17 2004

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization


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