TY - JOUR
T1 - Unknown input functional observability of descriptor systems with neutral and distributed delay effects
AU - Bejarano, Francisco Javier
AU - Zheng, Gang
N1 - Publisher Copyright:
© 2017 Elsevier Ltd
PY - 2017/11
Y1 - 2017/11
N2 - In this paper a general class of linear systems with time-delays is considered, which includes linear classical systems, linear systems with commensurate delays, neutral systems and singular systems with delays. After given a formal definition of functional backward observability (BO), an easily testable condition is found. The fulfillment of the obtained condition allows for the reconstruction of the trajectories of the system under consideration using the actual and past values of the system output and some of its derivatives. The methodology we follow consists in an iterative algorithm based upon the classical Silverman algorithm used for inversion of linear systems. By using basic module theory we manage to prove that the proposed algorithm is convergent. A direct application of studying functional observability is that a condition can be derived for systems with distributed delays also, we do this as a case of study. The obtained results are illustrated by two examples, one is merely academic but illustrates clearly the kind of systems which the proposed methodology works for and the other is a practical system with distributed delays.
AB - In this paper a general class of linear systems with time-delays is considered, which includes linear classical systems, linear systems with commensurate delays, neutral systems and singular systems with delays. After given a formal definition of functional backward observability (BO), an easily testable condition is found. The fulfillment of the obtained condition allows for the reconstruction of the trajectories of the system under consideration using the actual and past values of the system output and some of its derivatives. The methodology we follow consists in an iterative algorithm based upon the classical Silverman algorithm used for inversion of linear systems. By using basic module theory we manage to prove that the proposed algorithm is convergent. A direct application of studying functional observability is that a condition can be derived for systems with distributed delays also, we do this as a case of study. The obtained results are illustrated by two examples, one is merely academic but illustrates clearly the kind of systems which the proposed methodology works for and the other is a practical system with distributed delays.
KW - Descriptor systems
KW - Neutral delays
KW - Observability
KW - Systems with time-delays
KW - Unknown inputs
UR - http://www.scopus.com/inward/record.url?scp=85027841713&partnerID=8YFLogxK
U2 - 10.1016/j.automatica.2017.07.044
DO - 10.1016/j.automatica.2017.07.044
M3 - Artículo
SN - 0005-1098
VL - 85
SP - 186
EP - 192
JO - Automatica
JF - Automatica
ER -