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How the choice of the observable may influence the analysis of nonlinear dynamical systems. (English) Zbl 1099.37521
This paper discusses issues relating to the observability and controllability of nonlinear dynamical systems. Using the Rössler system, the authors show that a more general definition of the observability matrix is the Jacobian matrix of the coordinate transformation between the original phase space and the differential embedding induced by the observable. Some explicit examples are treated and the authors show that the more general definition of the observability matrix in some cases allows better indications concerning the ability to obtain a global model from a given observable.

37N99 Applications of dynamical systems
93B07 Observability
93B05 Controllability
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
93C10 Nonlinear systems in control theory
Full Text: DOI
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