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Observability and Detectability of Singular Linear Systems with Unknown Inputs

Francisco Javier Bejarano 1 Thierry Floquet 1, 2, 3 Wilfrid Perruquetti 1, 2, 3 Gang Zheng 1, 2
1 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
2 SyNeR - Systèmes Non Linéaires et à Retards
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : In this paper the strong observability and strong detectability of a general class of singular linear systems with unknown inputs are tackled. The case when the matrix pencil is non-regular is comprised (i.e., more than one solution for the differential equation is allowed). It is shown that, under suitable assumptions, the original problem can be studied by means of a regular (non-singular) linear system with unknown inputs and algebraic constraints. Thus, it is shown that for purposes of analysis, the algebraic equations can be included as part of an extended system output. Based on this analysis, we obtain necessary and sufficient conditions guaranteeing the observability (or detectability) of the system in terms of the zeros of the system matrix. Corresponding algebraic conditions are given in order to test the observability and detectability. A formula is provided that expresses the state as high order derivative of a function of the output, which allows for the reconstruction of the actual state vector. It is shown that the unknown inputs may be reconstructed also.
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https://hal.inria.fr/hal-00753706
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Submitted on : Wednesday, March 8, 2017 - 11:46:57 PM
Last modification on : Wednesday, October 14, 2020 - 3:47:16 AM
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Francisco Javier Bejarano, Thierry Floquet, Wilfrid Perruquetti, Gang Zheng. Observability and Detectability of Singular Linear Systems with Unknown Inputs. Automatica, Elsevier, 2013, 49 (3), pp.6. ⟨hal-00753706⟩

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