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On observability of chaotic systems: An example. (English) Zbl 0733.93009

Robust control of linear systems and nonlinear control, Proc. Int. Symp. Math. Theory Networks Syst., MTNS, Vol. II, Amsterdam/Neth. 1989, Prog. Syst. Control Theory 4, 489-496 (1990).
Summary: [For the entire collection see Zbl 0723.00047.]
The concept of observability of a special chaotic system, namely the dyadic map, is studied here in case the observation is not exact. The usual concept of observable subspace does not distinguish among the behaviour of different models. It turns out that a suitable extension of this concept can be obtained using the idea of Hausdorff dimension. It is shown that this dimension increases as the observation error becomes smaller, and is equal to one only if the system is observable.

MSC:

93B07 Observability

Citations:

Zbl 0723.00047