Variants of nonlinear normal form observer design

Schaffner, Johanna; Zeitz, Μ.

doi:10.1007/bfb0109926

Cited by 15 publications

(14 citation statements)

References 19 publications

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“…For systems having this form, there are several techniques available to design exponential observers (for instance extended Luenberger observer [6][7][8], extended Kalman observer [9], high-gain observer [10,11]). For systems which are not written in form (1), the key state transformation is given by the map: …”

Section: )mentioning

confidence: 99%

Design of exponential observers for nonlinear systems by embedding

Rapaport¹,

Maloum²

2004

Intl J Robust & Nonlinear

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SUMMARYFor nonlinear systems in R n which are observable but not uniformly, we study how to design explicitly exponential observers, after having the system immersed in R m with m > n: The central issue concerns the determination of a lipschitzian extension in R m of the dynamics, which is defined exclusively on a subset of empty interior. We propose some constructive tools and illustrate their utility on a biological example.

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Section: )mentioning

confidence: 99%

Design of exponential observers for nonlinear systems by embedding

Rapaport¹,

Maloum²

2004

Intl J Robust & Nonlinear

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“…which proves the asymptotic stability of the error dynamics (14). For γ = 0, the Riccati inequality (15) becomes a Lyapunov inequality.…”

Section: Convergence Of Structured Systemsmentioning

confidence: 97%

“…His work has been extended into several directions such as observer design for time-varying and nonlinear systems [3]- [6], the simultaneous adaption of known parameters [7], [8], or the design of unknown input observers [9], [10] as well as functional observers [11], [12]. Several techniques for nonlinear observer design are subject to restrictive existence conditions [13] or require complicated calculations [14]. The particular feature of (1) is the decomposition of the system's dynamics into a linear and a nonlinear part.…”

Section: Introductionmentioning

confidence: 99%

Structure matters — Some notes on high gain observer design for nonlinear systems

Röbenack

2012

International Multi-Conference on Systems, Sygnals &Amp; Devices

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This paper deals with high gain observer design for Lipschitz nonlinear systems. High gain observers are very popular in applications because of their simple implementation with a constant observer gain. In practice, the gain is usually chosen based on eigenvalue placement sufficiently far in the complex left half-plane, where the convergence of the nonlinear observer is verified by simulation. Although this strategy works well in many applications, the exact choice of the observer gain is more complicated. In particular, existing design methods often result in a severe restriction of the maximum allowed Lipschitz constant. In many cases, these bounds on the Lipschitz constant are very conservative. We will show that the maximum admissible Lipschitz constant can be increased significantly if the structure of the system is taken into consideration.

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“…M. Such a map is called a semi-diffeomorphism (Xia and Zeitz 1997). Using it as coordinate transformation z ¼ FðxÞ, x ¼ F À1 ðzÞ, system (2) becomes (Schaffner and Zeitz 1999) …”

Section: Trajectory Semi-equivalencementioning

confidence: 99%

“…A local observer can be designed for system (1) if its linearization about an operating point is observable or at least detectable. In fact, most non-linear observer design methodologies make this assumption (Walcott et al 1987, Krener 1994, Schaffner and Zeitz 1999. However, no smooth observer exists if the linearization has an undetectable mode (Xia and Gao 1988).…”

Section: Introductionmentioning

confidence: 98%