A new methodology to design preserving order observers for a class of nonlinear systems, in absence and in presence of perturbations, is proposed. The preserving order observers are those whose estimates always stay above or below the true trajectory of the state. The design methodology combines two important systemic properties: dissipativity and cooperativity. The first is used to assure the convergence of the estimation error dynamics. Cooperativity is the basic property of the error dynamics in order to assure the order preserving properties of the observer. The design of these observers can be reduced, in most cases, to Linear Matrix Inequalities (LMI).
This paper studies the problem of designing interval observers for a family of discrete‐time nonlinear systems subject to parametric uncertainties and external disturbances. The design approach states that the interval observers are constituted by a couple of preserving order observers, one providing an upper estimation of the state while the other provides a lower one. The design aim is to apply the cooperative and dissipative properties to the discrete‐time estimation error dynamics in order to guarantee that the upper and lower estimations are always above and below the true state trajectory for all times, while both estimations asymptotically converge towards a neighborhood of the true state values. The approach represents an extension to the original method proposed by the authors, which focuses on the continuous‐time nonlinear systems. In some situations, the design conditions can be formulated as bilinear matrix inequalities (BMIs) and/or linear matrix inequalities (LMIs). Two simulation examples are provided to show the effectiveness of the design approach.
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