SummaryThis paper is concerned with the design of an LMI‐based discrete‐time nonlinear state observer for an anaerobic digestion model. In presence of disturbances in both the dynamics of the model and the output measurement signals, the... more
SummaryThis paper is concerned with the design of an LMI‐based discrete‐time nonlinear state observer for an anaerobic digestion model. In presence of disturbances in both the dynamics of the model and the output measurement signals, the proposed observer robustly estimates all state variables including bacteria concentrations, which are costly and difficult to measure. In the goal to increase applicability of the proposed observer for other systems, we present the theoretical results in a general way. First, due to the use of Young's inequality in a convenient way, we get new sufficient conditions, expressed in terms of bilinear matrix inequalities (BMIs), ensuring the criterion. Then, to render the BMIs convex, two alternative solutions are proposed, where both lead to linear matrix inequality (LMI) conditions. It is shown analytically and numerically that these two solutions provide less conservative LMI conditions compared to the existing methods in the literature. To valida...
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This paper concerns the bounded real lemma for discrete-time descriptor systems. A new formulation of the bounded real lemma for these systems is given, it extends the recent results presented in Zhang, Xia and Shi (2008) and gives... more
This paper concerns the bounded real lemma for discrete-time descriptor systems. A new formulation of the bounded real lemma for these systems is given, it extends the recent results presented in Zhang, Xia and Shi (2008) and gives necessary and sufficient conditions in strict LMI (linear matrix inequality) more suitable for the control design than those presented in Zhang et al. (2008). An application to the H∞ control design is given. A numerical example is presented to show the applicability of our approach.
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A recursive state estimator for linear singular systems is derived from the least squares estimation problem. Regularity of the matrix pencil (sE - A) is not required and state matrices E and A can be rectangular.
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ABSTRACT This paper deals with the H ∞ filtering problem for a class of nonlinear systems. This class of nonlinear systems is composed of a bilinear part and of a lipschitzian one. The use of an unbiasedness condition for the bilinear... more
ABSTRACT This paper deals with the H ∞ filtering problem for a class of nonlinear systems. This class of nonlinear systems is composed of a bilinear part and of a lipschitzian one. The use of an unbiasedness condition for the bilinear part (called quasi unbiasedness condition) permits to parameterize the filter matrices through a single gain. Two LPV (Linear Parameter Varying) extensions of the bounded real lemma are used to solve the filtering problem. This approach reduces the conservatism inherent to the boundedness of the inputs. Then the filtering solution is expressed in terms of LMI (Linear Matrix Inequality) to be verified at the vertices of a polytope. A numerical example is finally given to illustrate our approach.
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This paper is concerned with the design of linear functional state observers for systems with delays in state variables. In particular, the necessary and sufficient conditions for the existence of the rth-order observers are given.... more
This paper is concerned with the design of linear functional state observers for systems with delays in state variables. In particular, the necessary and sufficient conditions for the existence of the rth-order observers are given. Sufficient conditions for the stability dependent of delays and stability independent of delays are derived using linear matrix-in-equality formulation. A systematic design method of these
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The problem under investigation is the design of an observer for non uniformly observable bilinear systems. The bilinear system can be separated into two subsystems: one is uniformly observable and the other is not. A high gain observer... more
The problem under investigation is the design of an observer for non uniformly observable bilinear systems. The bilinear system can be separated into two subsystems: one is uniformly observable and the other is not. A high gain observer is designed for the “observable part” while an unbiased observer is synthesized for the “unobservable part”. The exponential stability of the observation error for the two-stage observer is proved.
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ABSTRACT In this paper, the Group Mean Square Synchronization (GMSS) of a new class of adaptive Complex Dynamical Network (CDN) with Limited Stochastic Perturbation (LSP) and interval Time-Varying Delays (TVD) is investigated. The... more
ABSTRACT In this paper, the Group Mean Square Synchronization (GMSS) of a new class of adaptive Complex Dynamical Network (CDN) with Limited Stochastic Perturbation (LSP) and interval Time-Varying Delays (TVD) is investigated. The zero-mean real scalar Brownian Motion (BM) with LSP is also discussed. In this CDN, the weight configuration matrices are considered in two cases : TVD and Non-Time-Varying Delay (NTVD). The outer-coupling matrices are also assumed to be two cases : symmetric and dissymmetric. Based on the control theory and stochastic analysis such as : adaptive control method, Itô formula, Lyapunov Stability Theory (LST) and Kronecker product rules, the controllers nd adaptive schemes are constructed which let all nodes reach the GMSS asymptotically in the CDN. Finally, some examples of several complex chaotic systems are presented to demonstrate the proposed theoretical analysis.
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This paper investigates a discrete-time domain design of unknown input functional observer (UIFO) for discrete-time linear singular delayed systems. Note that both constant and variable delays are considered. The main procedure is based... more
This paper investigates a discrete-time domain design of unknown input functional observer (UIFO) for discrete-time linear singular delayed systems. Note that both constant and variable delays are considered. The main procedure is based on Lyapunov-Krasovskii stability theory, where the optimal gain in the functional observer is a solution of linear matrix inequalities (LMIs). Sufficient conditions for observer stability are proposed. The effectiveness of the proposed approach is illustrated by a numerical example.
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ABSTRACT This paper considers the H∞ dynamical observer-based control design for descriptor systems. The goal is to design a controller such that the closed loop system is stable while the transfer function from the disturbance to the... more
ABSTRACT This paper considers the H∞ dynamical observer-based control design for descriptor systems. The goal is to design a controller such that the closed loop system is stable while the transfer function from the disturbance to the controlled output of the dynamical error, satisfies a prescribed H∞ norm level. Conditions for the solvability of this problem are obtained in terms of a set of linear matrix inequalities (LMIs). A numerical example is given to illustrate the main contribution of this paper.
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In this paper, we present a new design of unknown input observers. Necessary and sufficient conditions are given for the existence of this observer for both minimum and non-minimum phase systems. This unknown input observer design is... more
In this paper, we present a new design of unknown input observers. Necessary and sufficient conditions are given for the existence of this observer for both minimum and non-minimum phase systems. This unknown input observer design is closely related to an exact model matching problem
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We present an H∞ reduced-order controller design method for bilinear systems, that ensures a local exponential stability and an L2-gain attenuation level. Synthesis parameters are provided to adjust the size of the domain of attraction... more
We present an H∞ reduced-order controller design method for bilinear systems, that ensures a local exponential stability and an L2-gain attenuation level. Synthesis parameters are provided to adjust the size of the domain of attraction and the attenuation level
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In this paper, a new robust unifiedH∞ dynamic observer (UDO) design for systems in the presence of time-varying uncertainty and disturbances is presented. The observer design method is derived from the solution of the liner matrix... more
In this paper, a new robust unifiedH∞ dynamic observer (UDO) design for systems in the presence of time-varying uncertainty and disturbances is presented. The observer design method is derived from the solution of the liner matrix inequality (LMI), based on the solution of the algebraic constraint obtained from the analysis of the estimation error. A numerical example is presented to show the performance of the proposed observer
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In this paper, an adaptive observer design with parameter identification for a nonlinear system with external perturbations and unknown parameters is proposed. The states of the nonlinear system are estimated by a nonlinear observer and... more
In this paper, an adaptive observer design with parameter identification for a nonlinear system with external perturbations and unknown parameters is proposed. The states of the nonlinear system are estimated by a nonlinear observer and the unknown parameters are also adapted to their values. Sufficient conditions for the stability of the adaptive observer error dynamics are derived in terms of linear matrix inequalities. Simulation results for chaotic Lorenz systems with unknown parameters in the presence of external perturbations are given to illustrate the effectiveness of our proposed approach.
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ABSTRACT This paper proposes a method of designing an unbiased functional observer for each subsystem of a large scale delay discrete-time system. The method uses a rewriting of the observation error to avoid the constraint (due to the... more
ABSTRACT This paper proposes a method of designing an unbiased functional observer for each subsystem of a large scale delay discrete-time system. The method uses a rewriting of the observation error to avoid the constraint (due to the interconnection terms) that generally arises in observer design for these systems. The approach that we use to express the observation error permits to use results on stabilization of large scale delay discrete-time systems to solve the problem. The proposed observers are free of the interconnection terms and the observation error are unbiased. Each observer gain is parameterized via a single gain matrix which is computed via LMI. A tractable algorithm permits to compute the proposed observer easily.
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This paper discusses a design procedure of an asymptotic reduced-order H∞ observer for a n-joint rigid robot manipulator. The possibility of estimating the joint angular velocities via the proposed observer is investigated, which provides... more
This paper discusses a design procedure of an asymptotic reduced-order H∞ observer for a n-joint rigid robot manipulator. The possibility of estimating the joint angular velocities via the proposed observer is investigated, which provides an asymptotic convergence of the reconstruction error, and attenuates the effect of the external disturbances on the robot model
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In this paper, we consider the H∞ observers design for singular bilinear systems. The approach is based on the parameterized solution of a set of constrained Sylvester equations. The results can be seen as the unification of the full... more
In this paper, we consider the H∞ observers design for singular bilinear systems. The approach is based on the parameterized solution of a set of constrained Sylvester equations. The results can be seen as the unification of the full order, the reduced order and minimal order observers design for singular bilinear systems. The parameters of these observers are obtained by solving an LMI.
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It is shown that the parity vector method defined by Chen and Zhang (1990) is equivalent to the innovation approach for a simple choice of the parity matrix.
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ABSTRACT This paper deals with the pole assignment problem for linear singular systems by using state feedback control. The solution of the nonlinear algebraic equation XA + XBXE = HXE is studied. Necessary and sufficient conditions of... more
ABSTRACT This paper deals with the pole assignment problem for linear singular systems by using state feedback control. The solution of the nonlinear algebraic equation XA + XBXE = HXE is studied. Necessary and sufficient conditions of existence of the solution are presented in this work. The link between the pole assignment problem and the solution of this equation is related. Applications to the constrained control problem of linear singular systems are also presented. Conditions of positive invariance are then established.
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PurposeThe purpose of this paper is to propose solutions for both discrete-time and frequency-domain designs of unbiased H 8 functional filters for discrete-time linear systems affected by bounded norm energy disturbances.... more
PurposeThe purpose of this paper is to propose solutions for both discrete-time and frequency-domain designs of unbiased H 8 functional filters for discrete-time linear systems affected by bounded norm energy disturbances. Design/methodology/approachThe ...
This paper provides a simple and systematic design method of reduced-order observers without internal delays for systems having a time delay in the state variables. Necessary and sufficient conditions for the existence of these observers... more
This paper provides a simple and systematic design method of reduced-order observers without internal delays for systems having a time delay in the state variables. Necessary and sufficient conditions for the existence of these observers are given
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... M. BOUTAYEB, M. DAROUACH, H. RAFARALAHY, G. KRZAKALA E m - CRAN CNRS UA 821 186, rue de Lorraine, Comes et Romain 54400 - FRANCE Abstract ... [31 S. Kaprielian and J. Turi, "An observer for a non linear descriptor... more
... M. BOUTAYEB, M. DAROUACH, H. RAFARALAHY, G. KRZAKALA E m - CRAN CNRS UA 821 186, rue de Lorraine, Comes et Romain 54400 - FRANCE Abstract ... [31 S. Kaprielian and J. Turi, "An observer for a non linear descriptor system," CDC Tucson, Arizona, pp. ...
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ABSTRACT This paper explores a new method for detecting cyber-attacks on a controller. Specifically, the proposed detector is based on invariant sets in order to determine whether an attacker has hijacked the controller and perpetrated a... more
ABSTRACT This paper explores a new method for detecting cyber-attacks on a controller. Specifically, the proposed detector is based on invariant sets in order to determine whether an attacker has hijacked the controller and perpetrated a cyber-attack. One particularity of this detection method is that few information about the controller is required. Thus, the detector becomes useful for a large range of control laws and its vulnerability can be reduced by limiting its accessibility. Finally, a simple but significant example is presented in order to show the benefits and the flaws of the proposed methodology.
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In this paper an H∞ decentralized observer-based control is proposed for large-scale uncertain nonlinear systems. These systems are coupled by N interconnected subsystems where the interconnections satisfy the quadratic constraints. The... more
In this paper an H∞ decentralized observer-based control is proposed for large-scale uncertain nonlinear systems. These systems are coupled by N interconnected subsystems where the interconnections satisfy the quadratic constraints. The proposed control is based on a new form of dynamic observer (DO) which generalizes the existing results on the proportional observer (PO) and the proportional integral observer (PIO). The design approach is derived from the solution of matrix inequality and based on the algebraic constraints obtained from the analysis of the estimation error. A numerical example is provided to show the effectiveness of the proposed control.
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In this paper, we propose a systematic approach to design reduced-order observers for time-delay systems. Necessary and sufficient conditions for the existence of such observers are derived. We also show that resolution of the well-known... more
In this paper, we propose a systematic approach to design reduced-order observers for time-delay systems. Necessary and sufficient conditions for the existence of such observers are derived. We also show that resolution of the well-known Sylvester equation is not required. A numerical example is given to show the performances of the proposed approach.
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Presents a simple solution to the optimal unbiased reduced-order (or functional) filtering problem for linear time-varying systems. Necessary and sufficient conditions for the existence of the obtained filter are given. Stability and... more
Presents a simple solution to the optimal unbiased reduced-order (or functional) filtering problem for linear time-varying systems. Necessary and sufficient conditions for the existence of the obtained filter are given. Stability and convergence conditions are developed for the time-invariant systems. Both continuous- and discrete-time cases are considered
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ABSTRACT
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... CRAN CNRS UA 82 1. UniversitC Henri Poincark Nancy I Rue de Lorraine 186, Comes et Romain 54400 - FRANCE E-Mail : preudhom@ acturus.ciril.fr ... [7] S. Kaprielian and J. Turi, An observer for a non linear descriptor system, CDC... more
... CRAN CNRS UA 82 1. UniversitC Henri Poincark Nancy I Rue de Lorraine 186, Comes et Romain 54400 - FRANCE E-Mail : preudhom@ acturus.ciril.fr ... [7] S. Kaprielian and J. Turi, An observer for a non linear descriptor system, CDC Tucson, Arizona (1992) 975-976. ...
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... [3] Benzaouia, A., Baddou, A. and Elfaiz, S. Piecewise linear constrained control for continuous-time systems: The maximal admissible domain. ... 1999. [9] Chaabane, M., O. Bachelier, M. Souissi and D. Mehdi, Stability and... more
... [3] Benzaouia, A., Baddou, A. and Elfaiz, S. Piecewise linear constrained control for continuous-time systems: The maximal admissible domain. ... 1999. [9] Chaabane, M., O. Bachelier, M. Souissi and D. Mehdi, Stability and stabilization of continuous descriptor systems. ...
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... (19/08/2009). In this paper, we investigate the problem of stabilizing a class of nonlinear affine systems by using the generalization of Gronwall-Bellman lemma with two control laws : first a nonlinear state feedback and second a... more
... (19/08/2009). In this paper, we investigate the problem of stabilizing a class of nonlinear affine systems by using the generalization of Gronwall-Bellman lemma with two control laws : first a nonlinear state feedback and second a nonlinear observer-based control. ...
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ABSTRACT
Research Interests: Engineering, Mathematics, Computer Science, System Identification, Convergence, and 14 moreStability, Kalman Filter, Mathematical Sciences, Automatica, Dynamical System, Linear System, Observer, Discrete Time Control System, Covariance Matrix, Optimal Bayesian Estimation, Degree of Freedom, Autom, Scale Model, and Discrete time
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ACKNOWLEDGMENT only a straightforward matrix manipulation have been presented in [ 171 and [ 181. Observers for discrete-time descriptor systems have been developed in [14] and ~161, However. few results have been presented to design... more
ACKNOWLEDGMENT only a straightforward matrix manipulation have been presented in [ 171 and [ 181. Observers for discrete-time descriptor systems have been developed in [14] and ~161, However. few results have been presented to design observers