Observability Bifurcation Versus Observing Bifurcations

Boutat‐Baddas, Latifa; Barbot, Jean–Pierre; Boutat, Driss; Tauleigne, R.

doi:10.3182/20020721-6-es-1901.00248

Cited by 11 publications

(19 citation statements)

References 12 publications

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“…where for all 1 ≤ i ≤ n, f [2] i (z) and g [1] i (z) are, respectively, homogeneous polynomials of degree 2, respectively, 1 in components of z.…”

Section: Notations and Definitionsmentioning

confidence: 99%

“…Definition 3 (i) The component f [2] (z) + g [1] (z)u is the quadratic part of system (6). (ii) A quadratic transformation is a diffeomorphism of the form:…”

Section: Notations and Definitionsmentioning

confidence: 99%

“…Note that the output-injection term is canceled in the observation error dynamic for system (2). The diffeomorphism θ must satisfy the following first-order partial differential equation:…”

Section: Introductionmentioning

confidence: 99%

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Observability analysis by Poincaré normal forms

Boutat‐Baddas¹,

Boutat

Barbot

2009

Math. Control Signals Syst.

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International audienceThis paper deals with quadratic equivalence, normal forms of observability, characteristic matrices and normal quadratic numbers for nonlinear Single-Input Single-Output (SISO) systems. We investigated both cases; nonlinear systems linearly observable and nonlinear systems with one linear unobservable mode. Particularly, the effect of the normal quadratic numbers on the observer design is pointed out. Finally, a faster observability analysis is proposed using characteristic matrices and normal quadratic numbers. Throughout the paper, academic examples as well as bio-reactor example highlight our purpose

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“…where for all 1 ≤ i ≤ n, f [2] i (z) and g [1] i (z) are, respectively, homogeneous polynomials of degree 2, respectively, 1 in components of z.…”

Section: Notations and Definitionsmentioning

confidence: 99%

“…Definition 3 (i) The component f [2] (z) + g [1] (z)u is the quadratic part of system (6). (ii) A quadratic transformation is a diffeomorphism of the form:…”

Section: Notations and Definitionsmentioning

confidence: 99%

See 1 more Smart Citation

Observability analysis by Poincaré normal forms

Boutat‐Baddas¹,

Boutat

Barbot

2009

Math. Control Signals Syst.

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“…Lemma 3.2 The QDTOMC is invariant by a quadratic coordinates change and strict output injection (9).…”

Section: Left Invertibility Normal Formmentioning

confidence: 99%

Discrete-time Normal Form for Left Invertibility Problem

Djemaï

Barbot

Belmouhoub

2009

European Journal of Control

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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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“…As already mentioned above, chaotic signals and systems for private or secured communications have been investigated with increasing interest in the last few years (see references of authors [1], [2], [3], [4]). The advantage of using methods based on chaos theory lies in the high level of security chaotic systems offer as compared with traditional encryption techniques.…”

Section: Introductionmentioning

confidence: 99%