A high gain observer for a class of uniformly observable systems

Bornard, G.; Hammouri, Hassan

doi:10.1109/cdc.1991.261650

Cited by 155 publications

(77 citation statements)

References 10 publications

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“…where F (u, z) is the dynamics of systems (3,7) and K is a constant vector which does not depend on the input. In Section 3, we will extend the above observer design (9) to a class of MIMO nonlinear systems which generalizes systems (7).…”

Section: • Some Well-known Observability Notionsmentioning

confidence: 99%

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Nonlinear observers for locally uniformly observable systems

Hammouri

Farza

2003

ESAIM: COCV

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Abstract. This paper deals with the observability analysis and the observer synthesis of a class of nonlinear systems. In the single output case, it is known [4-6] that systems which are observable independently of the inputs, admit an observable canonical form. These systems are called uniformly observable systems. Moreover, a high gain observer for these systems can be designed on the basis of this canonical form. In this paper, we extend the above results to multi-output uniformly observable systems. Corresponding canonical forms are presented and sufficient conditions which permit the design of constant and high gain observers for these systems are given.Mathematics Subject Classification. 37N35, 93Bxx.

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Section: • Some Well-known Observability Notionsmentioning

confidence: 99%

“…Moreover, using this canonical form, the authors designed a high gain observer. Using similar canonical forms, many authors have studied separately high gain observer synthesis (see for instance [3,6]). …”

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confidence: 99%

Nonlinear observers for locally uniformly observable systems

Hammouri

Farza

2003

ESAIM: COCV

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“…Most of the published works deal with a class of linear systems with additive nonlinearity characterized by a non linear term in the state and output equation, that are assumed to fulfill a Lipschitz condition. The use of linear matrix inequalities has made possible to address the design of observers for that class of systems surpassing the drawbacks of previous approaches, where a high gain was needed to compensate for the non linear term, as initially proposed in [3]. Another alternative is the use of proportional/integral observers [1], that is, observers where the corrective action is proportional to the observation error and its integral, leading to a more complex observer dynamics.…”

Section: Introductionmentioning

confidence: 99%

H∞ Observer Design for a Class of Nonlinear Discrete Systems

Peñarrocha

Sanchis

Albertos

2009

European Journal of Control

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In this paper, the problem of observing the state of a class of discrete nonlinear system is addressed. The design of the observer is dealt with using H∞ performance techniques, taking into account disturbance and noise attenuation. The result is an LMI optimization problem that can be solved by standard optimization techniques. A design strategy is proposed based on the available disturbances information.

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“…This strategy was first validated in simulation for a three link biped without feet, using nonlinear high gain observers and a nonlinear observer based on sliding modes with a finite time convergence (Lebastard et al 2006a) and (Lebastard et al 2006b), for walking gaits composed of single support phases and impacts. The main drawback with this family of observers is that, when only some of the degrees of freedom are measured, a state coordinates transformation is necessary to design their canonical form (Gauthier & Bornard 1981;Krener & Respondek 1985;Bornard & Hammouri 1991;Plestan & Glumineau 1997). In this chapter, the observer is an extended Kalman filter and it is applied to SemiQuad, a prototype walking robot built at our institute.…”

Section: Introductionmentioning

confidence: 99%