An interval observer for uncertain continuous‐time linear systems

Abstract

Summary To design robust interval observers for uncertain continuous‐time linear systems, a new set‐integration approach is proposed to compute trajectory tubes for the estimation error. Because this approach, the order‐preserving condition on the dynamics of the estimation error is no longer required. Therefore, scriptH∞ synthesis methods can be used to compute observer gains that reduce the impact of the system uncertainties on the accuracy of the estimated state enclosures. The performance of the proposed approach is showcased through illustrative numerical examples.

Hydrogen sensor fault detection in a dark fermenter based on an interval observer and adaptive thresholds

“…In this paper, we consider the interval observer structure, reported in (Meslem et al, 2020), for a class of linear systems in presence of perturbations. The interval observer provides the upper and lower bounds for the trajectory of the dark fermenter state.…”

“…Based on the formulation in (Meslem et al, 2020), we firstly consider the linear observer with the Luenberger structure for the dark fermenter linear model presented in (Torres and Avilés, 2021), described as follows…”

Stabilizing a class of nonlinear parameter‐varying systems using interval observer based on a piecewise framework

“…where x l , x u ∈ R n are the state variables of the interval observer, L l , L u ∈ R n×r are observer gains, and F l , F u ∈ R n×n are the gains defined to satisfy the monotone systems theory and in contrast to the method presented in Reference 29, provide additional degrees of freedom for the positivity of the state matrix of error dynamic in the following theorem that provides sufficient conditions for the existence of interval observer (11).…”

“…Therefore, these kinds of observers are very compatible with the structure of the parameter-varying systems in which knowing the exact values of the system states is a challenging task. Consequently, most papers published in the field of interval observers were dedicated to the parameter-varying systems in both discrete 8,9 and continuous [10][11][12] cases. The real states of the plant will be guaranteed to be in the interval between the lower and upper extremes for all the times by achieving the positivity of the lower and upper bound errors which will be met by the monotone systems theory.…”

Further results on the design of a class of discrete‐time set‐valued state estimators

“…Recently, in References 24,25, based on interval extension of the analytic expressions of the state response of linear (discrete/continuous‐time) systems, new methods to design interval‐based state estimators have been proposed. The new way to design set‐membership state estimators offers two main advantages.…”