An observability form for linear systems with unknown inputs

Floquet, Thierry; Barbot, Jean–Pierre

doi:10.1080/00207170500472909

Cited by 29 publications

(36 citation statements)

References 19 publications

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“…In [24], the authors presented an observation algorithm in order to put a linear system with unknown inputs in a set of block triangular observable forms, even if the matching condition was not fulfilled, and a finite time sliding mode observer was designed in order to estimate the state and the unknown inputs in [25]. The main idea of this algorithm is to take advantage of some equivalent output injections in order to generate fictitious outputs such that the system can be transformed into a set of block observable triangular forms.…”

Section: Extension Of the Matching Condition For Nonlinear Systemsmentioning

confidence: 99%

Super twisting algorithm-based step-by-step sliding mode observers for nonlinear systems with unknown inputs

Floquet

Barbot

2007

International Journal of Systems Science

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179

107

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. Super twisting algorithm based step-by-step sliding mode observers for nonlinear systems with unknown inputs. International Journal of Systems Science, Taylor Francis, 2007, 38 (10), pp.803-815. inria-00128137v2 Super twisting algorithm based step-by-step sliding mode observers for nonlinear systems with unknown inputsThis paper highlights the interest of step-by-step higher order sliding mode observers for MIMO nonlinear systems with unknown inputs. A structural matching condition, stating on the possibility to design such observers and to reconstruct the unknown inputs, is derived. A finite time sliding mode observer, based on the hierarchical use of the super twisting algorithm, is developed. Then, it is shown that this observer is of interest in the field of hybrid systems and systems with observability singularities. Lastly, it is shown through an example how to relax the usual matching condition by the means of this type of finite time sliding mode observer.

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Section: Extension Of the Matching Condition For Nonlinear Systemsmentioning

confidence: 99%

Super twisting algorithm-based step-by-step sliding mode observers for nonlinear systems with unknown inputs

Floquet

Barbot

2007

International Journal of Systems Science

Self Cite

179

107

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“…Proof: By following similar steps as those used in the proof of Proposition 3.1, we can find G * ϕ i|t and H * ϕ i|t as (43), where λ * i is the optimal solution of the Lagrangian multiplier corresponding to constraint (42c). Indicated by the KKT conditions, either λ * i = 0, or constraint (42c) holds at equality.…”

Section: Distributed Minimum Variance Estimatormentioning

confidence: 99%

“…In [43], this condition is relaxed however, by identifying the various matrices, the relaxed condition results in rank(C i ) ≥ n, which can be realized only for rank(C i ) = n in our setting. Thus, if C i is full rank, observability is guaranteed and, moreover, we have that C i ν ϕ i|t is full column rank independently of the message loss process.…”

Section: Distributed Minimum Variance Estimatormentioning

confidence: 99%

Model based peer-to-peer estimator over wireless sensor networks with lossy channels

Fischione

Speranzon³

2015

Automatica

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In this paper, the design methods and fundamental performance analysis of an adaptive peer-to-peer estimator are established for networks exhibiting message losses. Based on a signal state model, estimates are locally computed at each node of the network by adaptively filtering neighboring nodes' estimates and measurements communicated over lossy channels. The computation is based on a distributed optimization approach that guarantees the stability of the estimator while minimizing the estimation error variance. The fundamental performance limitations of the estimator are established based on the variance of the estimation error in relation to the message loss process. Numerical simulations validate the theoretical analysis and illustrate the performance with respect to other estimators.

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“…The present work aims at the development of a systematic method leading to the finite time observation of a class of nonlinear systems with unknown inputs even if the observability matching condition is not fulfilled. To this end, the procedure given in [5] is extended to the nonlinear case. It also results in a constructive algorithm that transforms the system into a similar type of block triangular observable forms.…”

Section: Introductionmentioning

confidence: 99%

An observation algorithm for nonlinear systems with unknown inputs

2009

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This paper provides some new developments in the design of unknown input observers for nonlinear systems. An algorithm which states if the state and the unknown input of the system can be recovered in finite time is introduced. This algorithm leads to the transformation of the system into an extended block triangular observable form suitable for the design of finite time observers. The proposed method is useful to relax some restrictive conditions of existing nonlinear unknown input observer design procedures.

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An observability form for linear systems with unknown inputs

Cited by 29 publications

References 19 publications

Super twisting algorithm-based step-by-step sliding mode observers for nonlinear systems with unknown inputs

Super twisting algorithm-based step-by-step sliding mode observers for nonlinear systems with unknown inputs

Model based peer-to-peer estimator over wireless sensor networks with lossy channels

An observation algorithm for nonlinear systems with unknown inputs

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