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...

International audienceIn this paper, a linear matrix inequality (LMI) technique for state estimation of discrete-time, nonlinear switched descriptor systems is developed. The considered systems are composed of linear and nonlinear parts. An observer giving a perfect unknown input (UI) decoupled state estimation is proposed. Sufficient conditions of global convergence of observers are proposed. Numerical examples are given to illustrate this method

This study is dedicated to the design of observers for non-linear systems described by Takagi-Sugeno (T-S) multiple models with unmeasurable premise variables. Furthermore, this T-S structure can represent a larger class of non-linear systems compared to the T-S systems with measurable premise variables. Considering the state of the system as a premise variable allows one to exactly represent the non-linear systems described by the general form ˙x ¼ f (x, u). Unfortunately, the developed methods for estimating the state of T-S systems with measured premise variable are not directly applicable for the systems that use the state as a premise variable. In the present paper, firstly, the design of observers for T-S systems with unmeasurable premise variable is proposed and sufficient convergence conditions are established by Lyapunov stability analysis. The linear matrix inequality (LMI) formalism is used in order to express the convergence conditions of the state estimation error in terms of LMI and to obtain the gains of the observer. Secondly, the proposed method is extended in order to attenuate energy-bounded unknown inputs such as disturbances. An academic example is proposed to compare some existing methods and the proposed one.