TY - JOUR
T1 - Observability and detectability of singular linear systems with unknown inputs
AU - Bejarano, Francisco Javier
AU - Floquet, Thierry
AU - Perruquetti, Wilfrid
AU - Zheng, Gang
N1 - Funding Information:
This research has been financially supported by EU Interreg IV A 2 Mers Seas Zeeën Cross-border Cooperation Programme under SYSIASS project 06-020. For more details about the SYSIASS project see the project website www.sysiass.eu . F.J. Bejarano held a postdoctoral position at INRIA - Nord Europe with the ALIEN team, from October 2010 to September 2011, period during which this work was produced.
PY - 2013/3
Y1 - 2013/3
N2 - 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.
AB - 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.
KW - Algebraic observability
KW - Singular systems
KW - Strong detectability
KW - Strong observability
UR - http://www.scopus.com/inward/record.url?scp=84875217114&partnerID=8YFLogxK
U2 - 10.1016/j.automatica.2012.11.043
DO - 10.1016/j.automatica.2012.11.043
M3 - Artículo
SN - 0005-1098
VL - 49
SP - 793
EP - 800
JO - Automatica
JF - Automatica
IS - 3
ER -