On macromodeling of nonlinear systems with time periodic coefficients

S. C. Sinha, Sangram Redkar, Eric A. Butcher

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Some new techniques for reduced order (macro) modeling of nonlinear systems with time periodic coefficients are discussed in this paper. The dynamical evolution equations are transformed using the Lyapunov-Floquet (L-F) transformation such that the linear parts of the new set of equations become time-invariant. The techniques presented here reduce the order of this transformed system and all original states are obtained via the appropriate transformations. This macromodel preserves the desired stability and bifurcation characteristics of the original large-scale system and due to relatively few states; it is suitable for simulation and controller design. In this work, methodologies based on linear and nonlinear projections as well as 'time periodic invariant manifold' idea are presented. The invariant manifold technique yields a 'reducibility condition' that determines when an accurate nonlinear order reduction is possible. A comparative study of these order reduction methods is also included. These techniques are compared by means of time traces and Poincaré maps. A numerical error analysis is also included and advantages and limitations are discussed by means of a practical example.

Original languageEnglish (US)
Pages (from-to)510-530
Number of pages21
JournalCommunications in Nonlinear Science and Numerical Simulation
Issue number4
StatePublished - Jul 2006


  • Lyapunov-Floquet (L-F) transformation
  • Nonlinear time periodic systems
  • Order reduction

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Applied Mathematics


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