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The purpose of this paper is to propose solutions for both discrete‐time and frequency‐domain designs of unbiased H_∞ functional filters for discrete‐time linear systems affected by bounded norm energy disturbances.

The discrete‐time procedure design is based on the unbiasedness of the functional filter using a Sylvester equation; then the problem is expressed in a singular system one and is solved in terms of linear matrix inequalities (LMIs). The frequency procedure design is derived from discrete‐time domain results by defining some useful matrix fraction descriptions and mainly, establishing the useful and equivalent form of the connecting relationship that parameterizes the dynamics behavior between discrete‐time and z‐domain.

The performance of the proposed approach is illustrated with the aid of a practical example. The proposed methods are easily implementable and concern a more general class of systems, as the transformation of the system in a singular one permits to treat the problem of perturbance advanced.

First, the order of this filter is equal to the dimension of the vector to be estimated, which is benefit in case of control purpose (reduction of time calculation comparing to the full order one). Second, all recent works on the functional filtering consider systems which permit to avoid to have advanced perturbation term in the error dynamics; the authors propose here an approach which resolves the H_∞ filtering problem even when the term is present. In addition, it permit to consider more general class of discrete‐time systems. Furthermore, the LMI approaching the discrete‐time case permits to handle with more general problem (H_∞, L₂−H_∞) than the classical Riccati one.

The purpose of this paper is to propose a decentralized observer for large‐scale singular systems.

In this paper, the authors investigate the problem of observers' design for large‐scale singular systems. The proposed decentralized observer is based on a new parameterization of the generalized Sylvester equation solution. The considered system is partitioned into small‐sizes interconnected subsystems with unknown interconnections.

A decentralized observer based on new parameterization of generalized Sylvester equation. The performance of the proposed approach is illustrated by a numerical example.

The proposed approach unites the full‐order, the reduced‐order and the minimal order observer design for large‐scale system. The conditions of the existence of this observer are given in the linear matrix inequalities (LMI) form.

Regarding the important roles of accuracy and robustness of tightly-coupled micro inertial measurement unit (MIMU)/global navigation satellite system (GNSS) for unmanned aerial vehicle (UAV). This study aims to explore the efficient method to improve the real-time performance of the sensors.

A covariance shaping adaptive Kalman filtering method is developed. For optimal performance of multiple gyros and accelerometers, a distribution coefficient of precision is defined and the data fusion least square method is applied with fault detection and identification using the singular value decomposition. A dual channel parallel filter scheme with a covariance shaping adaptive filter is proposed.

Hardware-in-the-loop numerical simulation was adopted, the results indicate that the gain of the covariance shaping adaptive filter is self-tuning by changing covariance weighting factor, which is calculated by minimizing the cost function of Frobenius norm. With the improved method, the positioning accuracy with tightly-coupled MIMU/GNSS of the adaptive Kalman filter is increased obviously.

The method of covariance shaping adaptive Kalman filtering is efficient to improve the accuracy and robustness of tightly-coupled MIMU/GNSS for UAV in complex and dynamic environments and has great value for engineering applications.

A covariance shaping adaptive Kalman filtering method is presented and a novel dual channel parallel filter scheme with a covariance shaping adaptive filter is proposed, to improve the real-time performance in complex and dynamic environments.