Identifiability for a Class of Discretized Linear Partial Differential Algebraic Equations

Cantó, Begoña; Coll, Carmen; Sánchez, Elena

doi:10.1155/2011/510519

Cited by 10 publications

(11 citation statements)

References 13 publications

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“…where p = 1 + 2α − β and q = −α (see [11] for more information). Note that (2) is a particular case of the more general linear time invariant system…”

Section: Statement Of the Problem And Preliminarymentioning

confidence: 99%

“…Thus, λ / ∈ σ( A n+1 ). To guarantee the stability of the perturbed system when the perturbed matrix is given by (11), using Proposition 3, we have the following result, which proof is straightforward. Proposition 9.…”

Section: Propositionmentioning

confidence: 99%

“…When a finite-difference method is applied to solve a partial differential equation the associated discrete model obtained shows structured matrices, see [11]. Motivated by the structure of the discrete approximation and the possibility that the coefficient matrices are subjected to some perturbations, in this paper, bounds are obtained assuming only perturbation with a fixed structure.…”

Section: Introductionmentioning

confidence: 99%

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Stability robustness of perturbed structured systems

Cantó

Coll

Sánchez

2014

Journal of the Franklin Institute

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In this paper, the robust stability problem of structured linear systems is analyzed. In order to preserve the structure of the initial system, the structure of the admissible perturbations is characterized. Frobenius and infinity matrix norms are used to study the robust stability of the system affected by different admissible perturbations. Upper bounds for the perturbations are obtained, which guarantee that the perturbed system remains stable. Finally, some examples are shown to illustrate the results.

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“…where p = 1 + 2α − β and q = −α (see [11] for more information). Note that (2) is a particular case of the more general linear time invariant system…”

Section: Statement Of the Problem And Preliminarymentioning

confidence: 99%

Section: Propositionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stability robustness of perturbed structured systems

Cantó

Coll

Sánchez

2014

Journal of the Franklin Institute

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“…It is an important step in the modeling process and it is necessary theoretical prerequisites to design the experiment and to identify the system. For that, it is possible estimate the unknown parameters of the model using experimental data (more information in [5]). Structural identifiability guarantees that the model parameters can be estimated uniquely, under ideal conditions.…”

Section: Identifiabilitymentioning

confidence: 99%

Structured parametric epidemic models

Cantó

Coll

Sánchez

2013

International Journal of Computer Mathematics

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A stage-structured model for a theoretical epidemic process that incorporates immature, susceptible and infectious individual in independent stages is formulated. In this analysis, an input interpreted as a birth function is considered. The structural identifiability is studied using the Markov parameters. Then, the unknown parameters are uniquely determined by the output structure corresponding to an observation of infection. Two different birth functions are considered: the linear case and the Beverton-Holt type to analyze the structured epidemic model. Some conditions on the parameters to obtain nonzero diseasefree equilibrium points are given. The identifiability of the parameters allows us determine uniquely the basic reproduction number R 0 and the stability of the model in the disease-free equilibrium is studied using R 0 in terms of the model parameters.

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“…Several authors have studied the identifiability problem using different techniques and some results on structural identifiability are given. In particular, if we consider the Markov parameters of system (4), V j (p) = A j (p)B, j ≥ 0, we can prove that the system is identifiable, that is all the parameters of the model can be known using experimental data (see [7]) and a characterization of structural identifiability of system (4) is given in [2].…”

Section: Preliminariesmentioning

confidence: 99%

On identifiability for chemical systems from measurable variables

et al. 2013

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The dynamics of the composition of chemical species in reacting systems can be characterized by a set of autonomous differential equations derived from mass conservation principles and some elementary hypothesis related to chemical reactivity. These sets of ordinary differential equations (ODEs) are basically non-linear, their complexity grows as much increases the number of substances present in the reacting media and can be characterized by a set of phenomenological constants (kinetic rate constants) which contains all the relevant information about the physical system. The determination of these kinetic constants is critical for the design or control of chemical systems from a technological point of view but the non-linear nature of the ODEs implies that there are hidden correlations between the parameters which maybe can be revealed with a identifiability analysis.

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Identifiability for a Class of Discretized Linear Partial Differential Algebraic Equations

Cited by 10 publications

References 13 publications

Stability robustness of perturbed structured systems

Stability robustness of perturbed structured systems

Structured parametric epidemic models

On identifiability for chemical systems from measurable variables

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