Remarks on strong observability and detectability of linear time delay systems with disturbances

Przyłuski, K. Maciej; Sosnowski, Andrzej

doi:10.1016/0167-6911(84)90020-3

Cited by 7 publications

(3 citation statements)

References 10 publications

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“…However, unlike nonlinear systems without delays, the analysis of properties for time-delay system is more complicated (see the surveys in Sename and Briat (2001) and Richard (2003)). For linear time-delay systems, various aspects of the observability problem have been studied in the literature, by different methods such as functional analytic approach (Bhat and Koivo (1976)), algebraic approach (Brewer et al (1986); Sontag (1976); Fliess and Mounier (1998)), and so on (Przyiuski and Sosnowski (1984)). The theory of non-commutative rings has been applied to analyze nonlinear time-delay systems firstly by Moog et al (2000) for the disturbance decoupling problem of nonlinear time-delay system, and for observability of nonlinear timedelay systems with known inputs by Xia et al (2002), for identifiability of parameter for nonlinear time-delay systems in Zhang et al (2006), and for state elimination and delay identification of nonlinear time-delay systems by Anguelova and Wennberga (2008).…”

Section: Introductionmentioning

confidence: 99%

Finite time observation of nonlinear time-delay systems with unknown inputs

Zheng

Barbot

Boutat

et al. 2010

IFAC Proceedings Volumes

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Section: Introductionmentioning

confidence: 99%

Finite time observation of nonlinear time-delay systems with unknown inputs

Zheng

Barbot

Boutat

et al. 2010

IFAC Proceedings Volumes

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“…Mounier et al (1997), Bellen et al (1999), Zheng and Frank (2002)). Some results on the observability problem of dynamical systems with timedelays can be found in Lee and Olbrot (1981); Olbrot (1981); Malek-Zavarei (1982); Przyiuski and Sosnowski (1984); Fliess and Mounier (1998); Sename (2001); Marquez-Martinez et al (2002); Sename (2005); Anguelova and Wennberg (2010); Zheng et al (2011); Bejarano and Zheng (2014).…”

Section: Introductionmentioning

confidence: 99%

Unknown input functional observability of descriptor systems with neutral and distributed delay effects

Bejarano

Zheng

2017

Automatica

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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.

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“…For linear time-delay systems, various aspects of the observability problem have been studied in the literature, by different methods such as functional analytic approach (Bhat and Koivo (1976)), algebraic approach (Brewer et al (1986); Sontag (1976); Fliess and Mounier (1998)), and so on (Przyiuski and Sosnowski (1984)). The theory of non-commutative rings has been applied to analyze nonlinear time-delay systems firstly by Moog et al (2000) for the disturbance decoupling problem of nonlinear time-delay system, and for observability of nonlinear timedelay systems with known inputs by Xia et al (2002), for identifiability of parameter for nonlinear time-delay systems in Zhang et al (2006), and for state elimination and delay identification of nonlinear time-delay systems by Anguelova and Wennberga (2008).…”

Section: Introductionmentioning

confidence: 99%