Interval observers design for singularly perturbed systems

Yousfi, B.; Raïssi, Tarek; Amairi, Messaoud; Aoun, Mohamed

doi:10.1109/cdc.2014.7039634

Cited by 8 publications

(3 citation statements)

References 27 publications

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“…Statement 6. If the t-family of fast subsystems (9) is completely observable, then for any ρ f > 0 there exists a ρ f -exponential observer (15).…”

Section: Observers For Subsystemsmentioning

confidence: 99%

“…(see reviews [9][10][11][12][13] and references there). For SPS, depending on the information about the small parameter and the needs of the applications, different formulations of observation problems can be considered: with a known value of the small parameter µ [14], for a 374 TSEKHAN known closed interval of values of the small parameter µ ∈ [µ, µ] ⊂ (0, µ 0 ] [15], for an unknown value of the small parameter µ [16]. Formulations are also distinguished depending on the composition of the components being evaluated: estimation of both slow and fast components, or only slow components (see [10] and references there).…”

Section: Introductionmentioning

confidence: 99%

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Composite Observer of a Linear Time-Varying Singularly Perturbed System with Quasidifferentiable Coefficients

Tsekhan

2024

ARC

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For a linear time-varying singularly perturbed system with a small parameter µ for a part of derivatives and quasi-differentiable coefficients, existence conditions are established and µ-asymptotic composite full- and reduced-order observers are constructed. The error in estimating a state with an arbitrary predetermined exponential decay rate converges to an infinitesimal value of the same order of smallness as the small parameter. The observer gain vector are expressed in terms of the gain vectors of subsystems of smaller dimension than the original one and independent of the small parameter, and the parameters of the original system are subject to weaker requirements than those previously known. A constructive algorithm for calculating the gain vector of a composite observer is presented.

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“…Statement 6. If the t-family of fast subsystems (9) is completely observable, then for any ρ f > 0 there exists a ρ f -exponential observer (15).…”

Section: Observers For Subsystemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Composite Observer of a Linear Time-Varying Singularly Perturbed System with Quasidifferentiable Coefficients

Tsekhan

2024

ARC

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“…27 The observer problem was first brought up by Porter 28 for linear systems with fast and slow modes; and has been thereafter thoroughly studied for both linear and nonlinear systems, mostly within the singular perturbation framework. 18,27,[29][30][31][32][33][34][35][36][37][38][39][40] Particularly, for linear two-time-scale systems, Yoo and Gajic 40 have recently proposed a linear observer design method. In their approach, the observer poles can be independently placed for the two fast and slow subsystems, by decomposing a singularly perturbed system through a series of linear transformations.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear observer design for two‐time‐scale systems

Duan

Kravaris

2020

AIChE Journal

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A two-time-scale system involves both fast and slow dynamics. This article studies observer design for general nonlinear two-time-scale systems and presents two alternative nonlinear observer design approaches, one full-order and one reduced-order.The full-order observer is designed by following a scheme to systematically select design parameters, so that the fast and slow observer dynamics are assigned to estimate the corresponding system modes. The reduced-order observer is derived based on a lower dimensional model to reconstruct the slow states, along with the algebraic slow-motion invariant manifold function to reconstruct the fast states. Through an error analysis, it is shown that the reduced-order observer is capable of providing accurate estimation of the states for the detailed system with an exponentially decaying estimation error. In the last part of the article, the two proposed observers are designed for an anaerobic digestion process, as an illustrative example to evaluate their performance and convergence properties.

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