This article aims at investigating distributed interval estimation methods for continuous-time linear time-invariant (LTI) systems. By allying a robust observer design method and interval analysis techniques, we develop a novel two-step interval estimation method for LTI systems whose outputs are measured by a series of nodes connected via a given directed graph. First, a distributed observer formed by a group of local observers is designed via an $H_{\infty } $ approach to obtain an accurate point-valued estimation. This estimation is completed by a reliable interval-valued estimation achieved by a rigorous set-valued analysis of the estimation error dynamics. In order to further enhance the accuracy of the estimated intervals, an elimination by inconsistency technique is applied to characterize the smallest common interval containing the actual state vector of the system. Compared with the existing distributed interval observer approaches, the proposed method can effectively enhance the tightness of the estimated state intervals. Simulation results are shown to support the theoretical findings.

This paper presents synthesis methods of Interval Observers (IO) for discrete-time linear switched systems subject to additive unknown-but-bounded process and measurement noises. The novelty of the proposed methods consists in the designing of IO directly in the original state coordinates of the systems. This enables to: (i) mitigating the wrapping effect related to the classical use of similarity transformations; (ii) avoiding the impulsive behavior of the estimation error dynamics, mostly generated by the use of different similarity transformation for each mode of the switched system; (iii) reducing online computational effort. In addition, Bilinear Matrix Inequalities (BMI) and Linear Matrix Inequalities (LMI) conditions are established to check the existence and to compute stabilizing observer gains. The obtained theoretical results are supported by numerical simulations.

In a bounded error context, a secure set-valued state estimator for a class of systems described by a linear discrete-time difference inclusion is introduced in this contribution. The proposed design approach is based on set-valued computation combined with elimination by consistency techniques. More formally, we will show that a fusion between data provided by a set-valued predictor and those generated by a set-valued estimator allows one: (i) To obtain guaranteed state enclosures in the presence of additive and bounded state disturbance and measurement noise; (ii) To be able to detect faulty behaviors of the system and (iii) To be insensitive to a certain class of cyber-attacks. A numerical example is introduced to illustrate the performance of the proposed secure set-valued state estimator.

In this work, an actuator fault detection problem for discrete-time Takagi–Sugeno fuzzy systems is tackled in a bounded error context where both state disturbances and measurement noise are assumed to be unknown but bounded with known bounds. First, a peak-to-peak performance synthesis method is applied to design a robust residual generator against the considered process disturbances and measurement noise. Meanwhile, an improved zonotopic approach is proposed to compute tight adaptive thresholds for residual evaluation. Then, a reliable set-membership fault detection strategy with the aid of generated residual signals and adaptive thresholds is introduced. Finally, the viability of the proposed method is demonstrated via a numerical simulation. Then, an experimentation on a 3-D Crane system is performed to show its practicability.

This note proposes the use of invariant relationships between the state variables of discrete-time systems to improve the tightness of a class of set-membership state estimators. Thanks to these relationships, contractor algorithms could be designed to discard almost all state vectors that are not compatible with the model-based predicted state enclosure. Moreover, this contribution introduces a less computational complexity algorithm to perform efficiently the prediction stage of the proposed set-valued state estimator.

In this contribution, interval extensions for both full-order and reduced-order unknown input observers are proposed for uncertain discrete time linear systems. The introduced interval estimators do not rely on the positive systems property of the estimation errors. They are mainly based on numerical schemes conceived to characterize in a rigorous way the reached set of some classes of uncertain dynamical systems. Thus, only the classical existence conditions of unknown input observers are needed to design their interval extensions. Interval analysis is used as a convenient tool to implement the proposed state estimation algorithms. However, other bounded geometrical sets could be also applied. Numerical examples are studied to highlight the effectiveness of the introduced interval estimators in the presence of both system's uncertainties and unknown inputs.

This work proposes a new approach to synthesize interval observers for uncertain systems. The main novelty introduced by this approach is to conceive an interval observer as a combination between a punctual observer and a set-membership characterization of the observation error. Compared with existing methods, this approach allows more flexibility for computing the observation gain matrix and so to design an interval observer with a desired convergence rate. Moreover, only the classical observability assumption is needed to apply the proposed interval observer design method. An illustrative example is presented to show the performance of this approach.