Global stability of nonlinear systems with temporal multidimensionality

Victor F. Dailyudenko

doi:10.1117/12.421179

21 March 2001 Global stability of nonlinear systems with temporal multidimensionality

Victor F. Dailyudenko

Proceedings Volume 4390, Applications and Science of Computational Intelligence IV; (2001) https://doi.org/10.1117/12.421179
Event: Aerospace/Defense Sensing, Simulation, and Controls, 2001, Orlando, FL, United States

Abstract

For integrated instability investigation, a sequence of functional matrixes multiplication is transformed by separation of elements describing linear and nonlinear transformations in delay difference map. A quantity of multiplications of diagonal matrixes is minimized by means of dividing initial functional matrix into diagonal, triangle and the matrix of unit cyclic shift. The analytical expressions for product matrix have been obtained and different approaches of reducing the product matrix to rarefied form have been investigated. The analytical scheme for calculating rarefied product matrix has been constructed, its operations are invariant to changing a common length of investigated time series and transformed segments. The developed model can be used for characteristic polynomial determination and for increasing efficiency of computational algorithm of Lyapunov exponents calculation.

Citation Download Citation

Victor F. Dailyudenko "Global stability of nonlinear systems with temporal multidimensionality", Proc. SPIE 4390, Applications and Science of Computational Intelligence IV, (21 March 2001); https://doi.org/10.1117/12.421179

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