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The purpose of this paper is to present the non‐fragile observer design method for nonlinear switched systems with time delay.

Based on dwell time approach and linear matrix inequalities (LMIs) technology, an exponential stability criterion for the delay switched system with Lipschitz nonlinearity is presented. By using the key technical lemma, the observer design problem can be transferred to the problem of solving a set of LMIs. Moreover, non‐fragile observer is designed by the Schur complement lemma, and the result is also transferred to LMIs, which can be easily realized by MATLAB toolbox.

Non‐fragile observer design is more effective than the common one and is robust to the observer gain variations.

The proposed non‐fragile observer guarantees the estimated state error dynamics can be exponentially convergent for observer gain perturbations.

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.