Reduced-order observer design for descriptor systems with unknown inputs

Darouach, Mohamed; Zasadzinski, Michel; Hayar, Mohamed

doi:10.1109/9.508918

Cited by 189 publications

(132 citation statements)

References 23 publications

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“…For a given Z, Θ is deduced from (32), the matrices N i , M i and L i are derived from (19), (23) and (24) respectively. This result unifies the results obtained, on the one hand, in the field of the descriptor systems with UI [6], [9], [10] and, on the other hand, in the field of the TS systems with UI [1]. It is useful because a TSDS cannot be reduced, either to a single singular system (it would not handle the nonlinearities due to the weighting functions h i ), or to a regular TS system (it would not handle the algebraic relation between the state variables).…”

Section: Corollarysupporting

confidence: 75%

Design of observers for Takagi–Sugeno descriptor systems with unknown inputs and application to fault diagnosis

Marx

Koenig

Ragot

2007

IET Control Theory &Amp; Applications

176

139

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This paper presents a method for state-estimation of Takagi-Sugeno descriptor systems (TSDS) affected by unknown inputs (UI). For ease of implementation's sake, the proposed observers are not in descriptor form but in usual form. Sufficient existence conditions of the unknown input observers are given and strict linear matrix inequalities (LMI) are solved to determine the gain of the observers. If the perfect unknown input decoupling is not possible, the UI observer is designed in order to minimise the L2-gain from the UI to the state estimation error. The two previous objectives can be mixed in order to decouple the estimation to a subset of the UI, while attenuating the L2 gain from the other UI to the estimation. The proposed UI observers are used for robust fault diagnosis. Fault diagnosis for TSDS is performed by designing a bank of observers. A simple decision logic and thresholds setting allow to determine the occurring fault. The results are established for both the continuous and the discrete time cases.The proposed method is illustrated by a numerical example. Index TermsTakagi-Sugeno systems, singular systems, state estimation, unknown input observers, fault diagnosis. I. INTRODUCTIONThe Takagi-Sugeno (TS) model proposed by [14] is a well-known structure to represent nonlinear systems into several linear fuzzy models. In the last two decades, the control and the observation of TS systems have become challenging problems that received a considerable amount of attention. In The descriptor formalism is very attractive for system modelling, as pointed out in [4], since it describes a wider class of systems including physical systems with non dynamic constraints (e.g. algebraic relations induced in interconnected systems such as power transfer networks or water distribution networks) or jump behaviour. The enhancement of the modelling ability is due to the structure of the dynamic equation which encompasses not only dynamic equations, but also algebraic relations.Since both TS and descriptor formalisms are attractive in the field of modelling, the TS representation has been generalised to descriptor systems. The stability and the design of state-feedback controllers for TS descriptor systems to the authors' knowledge, the design of UIO has not been treated in the generic case of TSDS. The aim of this paper is not only to generalise the existing works on UIO design to TSDS, but also to apply this new observer in the field of fault diagnosis of TSDS which has not been treated so far. This paper gives a simple extension to TSDS of the design of observers for the state estimation in the presence of unknown inputs (UI). Under some sufficient conditions, the design of the observer is reduced to the determination of a matrix. The choice of this parameter is performed by solving strict LMIs. If the estimation error cannot be decoupled from the UI, an L 2 observer is proposed to minimise the influence of the UI on the state estimation. The two design objectives can be mixed by decoupling the state estimatio...

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Section: Corollarysupporting

confidence: 75%

Design of observers for Takagi–Sugeno descriptor systems with unknown inputs and application to fault diagnosis

Marx

Koenig

Ragot

2007

IET Control Theory &Amp; Applications

176

139

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“…The observability problem of DS has been studied in papers like Yip and Sincovec (1981); Cobb (1984); Hou and Müller (1999). The same problem but including unknown inputs has been addressed in Paraskevopoulos et al (1992); Geerts (1993); Darouach et al (1996); Koenig (2005); Darouach and Boutat-Baddas (2008); Bejarano et al (2013). Such systems, as many others, may contain time-delay terms in the state, input, and/or system output (see, e.g.…”

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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“…However there exist few results dealing with the problem of observer design for singular systems with unknown inputs [10], [11], [12]. Most investigation have been devoted to designing Luenberger observers.…”

Section: Introductionmentioning

confidence: 99%

Observability and detectability analysis of singular linear systems with unknown inputs

Bejarano

Floquet

Perruquetti

et al. 2011

IEEE Conference on Decision and Control and European Control Conference

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Abstract-We study the observability problem of a general class of singular linear systems with unknown inputs. It is shown that, under some assumptions, the problem is equivalent to study the observability of a standard linear system with unknown inputs satisfying algebraic constraints. We obtain necessary and sufficient conditions for observability in terms of the zeros of the system matrix.Index Terms-Singular systems, strong observability, algebraic observability.

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Reduced-order observer design for descriptor systems with unknown inputs

Abstract: : A new method for the design of reduced-order observers for descriptor systems with unknown inputs is presented. The approach is based on the generalized constrained Sylvester equation. Sufficient conditions for the existence of the observer are given.

Cited by 189 publications

References 23 publications

Design of observers for Takagi–Sugeno descriptor systems with unknown inputs and application to fault diagnosis

Design of observers for Takagi–Sugeno descriptor systems with unknown inputs and application to fault diagnosis

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

Observability and detectability analysis of singular linear systems with unknown inputs

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