The controlled center dynamics of discrete time control bifurcations

This paper deals with the design of quadratic and higher order normal forms for the left invertibility problem. The linearly observable case and one-dimensional linearly unobservable case are investigated. The interest of such a study in the design of a delayed discrete-time observer is examined. The example of the Burgers map with unknown input is treated and a delayed discrete-time observer is designed. Finally, some simulated results are commented.

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“…Remark 4.3 In this paper, only the case of left invertibility, without "approximated zero dynamics" 2 is investigated [16].…”

Section: Left Invertibility Normal Formmentioning

confidence: 99%

“…The associated Quadratic discrete-time Normal Form (QDTNF), is then obtained: Delayed Observer Design: A model of an observer is proposed for system (16) allowing to recover x 2 from y. Thus, using delayed corrections on the first observer state, it is possible to ensure "the synchronization" of both systems.…”

Section: An Illustrative Example: the Burgers Mapmentioning

confidence: 99%

Discrete time normal form for the left invertibility problem

Belmouhoub

Djemaï

Barbot

2004

IFAC Proceedings Volumes

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“…These results complement those given in [13], in which stabilization is accomplished by using quadratic functions. Other methods related to the control or even anti-control of bifurcations in maps can be found in [5,[14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%