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In this contribution, a new approach to design interval observer for continuous-time linear systems is introduced. First, a more general structure than the classical Luenberger observer is proposed and extended to the interval case based on an explicit set integration method. Then, to obtain tight state enclosures, the computation of the design matrices involved in this new structure is formulated as a nonlinear constrained optimisation problem. In addition, using the symmetric property of interval vectors, a less complex form of the proposed interval observer is presented. On the other hand, compared to the conventional interval observers, no preserving order property on the dynamics of the estimation error is required to apply the introduced method. A numerical case study example is considered to illustrate the effectiveness of the proposed method and to compare its performance to that of a former method. [ABSTRACT FROM AUTHOR]

This article proposes a two‐step interval estimation method for continuous‐time linear time‐invariant systems with unknown but bounded disturbances and measurement noise. In the first step, H∞$$ {H}_{\infty } $$ method is used to design a robust reduced‐order observer that attenuates the impact of the system uncertainties on the estimation error. In the second step, a non‐conservative interval prediction of the estimation error is achieved by applying a symmetric set‐integration approach. The resulting tight set‐valued state estimation is obtained by combining the point estimation from the reduced‐order observer with the predicted estimation error set provided by the set‐integration method. Compared to the conventional methods, the proposed method is built on less‐restrictive design conditions, that allow one to deal with a large range of applications. On the other hand, numerical simulations show that the proposed method offers more precise interval estimation compared to an optimal reduced‐order interval observer selected from recent literature. [ABSTRACT FROM AUTHOR]

This paper is concerned with prescribed-time functional unknown input observer (PTFUIO) design for linear descriptor systems. First, by constructing two identical asymptotic convergence functional observers, a new PTFUIO is developed which can achieve an exact estimation within an arbitrarily prescribed time, where both the estimation accuracy and the convergence time pre-definition are independent of the initial conditions of the original system. Also, the necessary and sufficient conditions for the existence of such the PTFUIO are given in terms of the original system matrices which are easy to examine. Finally, numerical simulations are given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

An interval estimation method based on the reduced-order observer and peak-to-peak analysis is proposed for continuous-time linear time-invariant systems with disturbance and measurement noise. The proposed method consists of two steps. First, a reduced-order observer with L ∞ performance is designed to obtain point estimation. Second, interval estimation is achieved by integrating the obtained point estimation and the error interval estimation by peak-to-peak analysis. Steady-state gain optimisation in terms of linear matrix inequalities is used in both steps to improve the estimation accuracy of the proposed method. The superiority of the method over the reduced-order interval observer is illustrated through numerical simulations. [ABSTRACT FROM AUTHOR]

This paper studies the problem of sensor fault interval estimation for discrete-time linear system with unknown but bounded disturbances and noises. A descriptor system which is equivalent to the original system is constructed by considering the fault as an auxiliary state vector. Based on the augmented descriptor system, a zonotopic Kalman filter is designed to obtain the interval estimation of sensor fault. To improve estimation accuracy, we further propose a Frobenius norm minimisation method to design the gain matrix of zonotopic Kalman filter. Finally, numerical simulations of a quadruple-tank system are given to illustrate the effectiveness and superiority of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper proposes an interval estimation method for discrete-time linear systems by designing robust reduced-order observer with reachability analysis. First, the discrete-time linear system is transformed into a reduced-order system via a special equivalent transformation, which depends on the orthogonal procedure on the output matrix. Then, a kind of robust reduced-order observer is developed such that the states of the original discrete-time system can be indirectly estimated, where the H ∞ technique is used to attenuate the effects of disturbances. Based on the estimated states provided by the reduced-order observer, the interval estimation can be obtained by reachability analysis. A simulation example is given to illustrate that the proposed method of interval estimation has better performance than the full-order observer-based interval estimation. [ABSTRACT FROM AUTHOR]

Summary: This article investigates the problem of designing a distributed fault estimation observer (DFEO) for a given linear time invariant observed system with disturbances. The DFEO consists of a network of local fault estimation observers. The local observers at the network nodes are physically distributed and hence each of them has access to only part of the output of the observed system. Each local fault estimation observer communicates with its neighbors as prescribed by the given network graph. Both full order and reduced order DFEO's are presented in this article. A systematic design procedure for DFEO gains is addressed, enabling the estimation error dynamics to be robust against the effects of the external process disturbance and the derivative of the fault. The numerical design of our DFEO is amounts to solving an optimization problem with constraints of a bank of linear matrix inequalities. Finally, we illustrate the effectiveness of the proposed distributed fault estimation approach by means of a number of simulation results. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to present a methodology to design interval observers for discrete-time linear switched systems affected by bounded, but unknown disturbances. Two design techniques are presented. The first one requires that the observation error dynamics are nonnegative while the second one relaxes this restrictive requirement by a change of coordinates. Furthermore, ideas of using H ∞ formalism to compute optimal gains are proposed. Finally, illustrative examples highlight the performance of our methodology. [ABSTRACT FROM AUTHOR]

Summary: This article studies reachable set estimation for linear discrete‐time systems with time delay, which are influenced by unknown but bounded disturbances. We propose a novel reachable set estimation method based on zonotopes for the considered systems. The proposed method can estimate real‐time reachable set under nonzero initial conditions. In order to increase estimation accuracy, we propose an iterative method to reduce the conservatism caused by the couplings between reachable sets at different instants. The effectiveness of the proposed method is illustrated by three numerical simulations. [ABSTRACT FROM AUTHOR]

This paper investigates actuator fault detection and isolation for discrete-time linear descriptor systems. We propose a novel fault detection and isolation scheme based on a bank of H − / L ∞ fault detection observers (FDOs). Under the assumption that the disturbances are unknown but bounded, L ∞ analysis is used to attenuate the effects of disturbances. Meanwhile, the FDO is designed to be sensitive to the fault via considering the H − performance index in finite frequency domain. The design conditions of the proposed FDO are converted into solving a set of linear matrix inequalities. Furthermore, the residual evaluation based on a set-membership approach is proposed to reduce conservatism. Simulation results are provided to demonstrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

This study proposes an interval estimation method of actuator fault for linear discrete‐time system. An augmented descriptor system, which is equivalent to the original system, is formulated by letting the actuator fault term be an auxiliary state. Then, an H∞ fault estimation observer is constructed to attenuate the effect of unknown but bounded disturbances and measurement noise. By using interval analysis technique, the interval estimation of actuator fault can be obtained. Finally, a DC servo‐motor example is given to show the effectiveness and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

Summary: This paper considers H−/L∞ fault detection for discrete‐time linear parameter‐varying (LPV) systems with parametric uncertainty. In H−/L∞ fault detection scheme, residual generation and threshold computation are simultaneously designed. With consideration of H−/L∞ performance indices, the generated residual is sensitive to faults while robust against unknown disturbances. Furthermore, the L∞ performance provides a time‐varying threshold for residual evaluation. This paper proposes a novel H−/L∞ fault detection observer design method to handle actuator fault detection for LPV systems with parametric uncertainty. Sufficient conditions of the fault detection observer design in the finite‐frequency domain are derived as linear matrix inequalities. Numerical simulations are used to illustrate the effectiveness and superiority of the proposed fault detection observer design approach. [ABSTRACT FROM AUTHOR]

This paper studies fault detection problem in the finite-frequency domain for linear systems with parameter uncertainties. We design an fault detection observer to generate residual that is robust against disturbance and sensitive to a fault. In the design, we use the finite-frequency performance index to measure fault sensitivity and introduce performance index to measure the effect of disturbance on residual. The obtained fault detection observer exhibits a peak-to-peak disturbance attenuation performance, which provides a time-varying threshold for residual evaluation. Therefore the proposed design method integrates residual generation and threshold calculation together. To facilitate the observer design process, sufficient conditions of the proposed fault detection observer are formulated as a set of linear matrix inequalities. Numerical simulations are given to verify the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, an L∞ observer design method is proposed for linear system subject to parameter uncertainty and bounded disturbance. The proposed L∞ observer, which satisfies a peak‐to‐peak disturbances attenuation performance, is designed to overbound the estimation error. Moreover, sufficient conditions for the design of L∞ observer are derived and expressed in terms of linear matrix inequalities (LMIs). The novelty of the proposed method is that we develop an L∞ observer that not only can attenuate bounded disturbance but also provides an upper bound of estimation error norm. Simulation results are presented to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Sensor fault detection of discrete‐time descriptor systems with bounded disturbances is studied. The authors propose a new structure of a fault detection observer by augmenting the output, which can broaden the application scope. A H−/L∞ criterion is used to achieve the fault sensitivity and disturbance attenuation ability of the residual simultaneously. The residual generation and time‐varying threshold calculation are integrated together based on L∞ analysis. Furthermore, sufficient conditions for the H−/L∞ performance of the proposed observer are formulated in terms of linear matrix inequalities. Numerical simulations of a direct current motor and a flight vehicle are conducted to verify the applicability of the proposed fault detection observer design method. [ABSTRACT FROM AUTHOR]

This paper investigates an interval estimation method for discrete-time linear time-delay systems subject to unknown but bounded disturbances and noise. We utilize the state augmentation technique to decouple the time delays. The interval estimation problem for the time-delay system will be transformed into that for a delay-free state augmented system. We then propose a two-step method which consists of robust observer design and zonotope-based interval analysis to achieve interval estimation. In observer design, a T − N − L observer is used to provide more degrees of design freedom, whose robustness is characterized by H ∞ performance. Finally, a numerical example is provided to demonstrate the effectiveness and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes a novel interval observer design method for discrete-time linear systems with unknown but bounded disturbance and measurement noise. The proposed interval observer has a new structure that provides more design degrees of freedom. A direct method based on H ∞ technique is used to improve the accuracy of interval estimation. The design conditions are formulated into linear matrix inequalities, which can be efficiently solved. Two numerical examples are given to illustrate the design and validate the performance of the interval observers. [ABSTRACT FROM AUTHOR]

This paper studies interval estimation for discrete-time linear systems with unknown but bounded disturbances. Inspired by the parity space approach, we propose a point estimator with fixed-time convergence property. The estimator is combined with the zonotope-based interval analysis to achieve fast interval estimation. The parameter matrix in the estimator is optimized by minimizing the length of the edges of the outer box of the error zonotope. It is formulated as L 1 optimization problem and can be efficiently solved by linear programming. Comparison studies illustrate the superiority of the proposed method over existing techniques. [ABSTRACT FROM AUTHOR]

This paper deals with interval state estimation for discrete-time linear systems with known time-varying delay. The considered systems are subject to unknown but bounded disturbances and measurement noise in predefined zonotopes. The main contribution lies in the development of a two-step interval estimation method which integrates a robust observer design providing more degrees of design freedom with a zonotopic analysis technique. By introducing the H ∞ formalism in the observer design, the proposed method is effective in reducing the effects of unknown uncertainties and improving the estimation accuracy. Based on the designed observer, the interval estimation is guaranteed by a novel zonotopic analysis taking into account the effects of the time-delay on the system dynamics. By using zonotopes, the proposed approach is intuitive and is able to overcome the wrapping effects, which refers to the significant growth of the constructed set dimension in the propagation process. Numerical simulations of a two-stage chemical reactor with delayed streams are given to show the effectiveness and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the observer design problem for discrete-time descriptor systems is considered. For the discrete-time linear descriptor systems, the necessary and sufficient conditions for the existence and convergence of the proposed observer are given and proved, and a systemic design approach is presented via the linear matrix inequalities formulation. Furthermore, an extension to a class of nonlinear descriptor systems with Lipschitz constraints is investigated. Simulation examples are given to illustrate the estimation performance of the proposed method. [Copyright &y& Elsevier]

• Propose two prescribed time observers for LPV systems. • State estimation can be achieved in an arbitrarily prescribed time step. • The pole placement of observers only requires solving finite number of LMIs. This paper considers prescribed-time observer (PTO) designs for a class of linear parameter-varying (LPV) systems. Firstly, a full-order prescribed-time observer with time-varying gains is developed. The existence conditions are given in terms of linear matrix inequalities (LMIs). In addition, the reduced-order PTO is also considered in this paper. Moreover, it is shown that the existence conditions under which the full-order PTO exists can also guarantee the existence of a corresponding reduced-order PTO. The advantages of the full-order and the reduced-order PTOs over the existing asymptotic convergence observers are that (1) they can achieve exact estimations in almost any prescribed convergence time regardless of what the system initial values are. (2) the proposed time-varying gain PTOs can avoid the conservatism of the unknown input decoupling conditions brought about by the traditional polytopic LPV observer design methods. Finally, two examples are given to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper studies interval observer design for linear parameter-varying systems subject to uncertainties in parameters, input and output. Based on a general assumption that these uncertainties are unknown but bounded by known intervals, a novel interval observer is presented to estimate the bounds of state. To attenuate the effect of uncertainties and obtain tight state intervals, a novel L ∞ norm based design method is proposed. Numerical simulations are conducted to demonstrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper we consider the distributed estimation problem for continuous-time linear time-invariant (LTI) systems. A single linear plant is observed by a network of local observers. Each local observer in the network has access to only part of the output of the observed system, but also receives information on the state estimates of its neighbors.Each local observer should in this way generate an estimate of the plant state. In this paper we study the problem of existence of a reduced order distributed observer. We show that if the observed system is observable and the network graph is a strongly connected directed graph, then a distributed observer exists with state space dimension equal to N n − ∑ i = 1 N p i , where N is the number of network nodes, n is the state space dimension of the observed plant, and p i is the rank of the output matrix of the observed output received by the i th local observer. In the case of a single observer, this result specializes to the well-known minimal order observer in classical observer design. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the problem of Luenberger-like interval observer design for discrete-time descriptor linear system is investigated. In the first place, two ways in which the original descriptor system is transformed into general systems are given and the detectability of the equivalent general systems is discussed in detail. A new equivalent general system construction is developed and we prove that the detectability can be kept under this new equivalent transformation. After this, based on the new equivalent general system, a Luenberger-like interval observer is proposed. Finally, two simulation examples are given to demonstrate the correctness and the effectiveness of the proposed interval observer. [ABSTRACT FROM AUTHOR]