Jordan Canonical Form in Diagnosis and Estimation Problems

Zhirabok, Alexey; Зуев, А. В.; Filaretov, Vladimir; Shumsky, Alexey; Ir, Kim Chkhun

doi:10.1134/s0005117922090028

Cited by 8 publications

(6 citation statements)

References 22 publications

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“…The algebra of functions has four main ingredients: (1) relation of partial preorder ⪯, (2) two binary operations × and ⊕, (3) binary relation Δ, (4) and operators m and M. These ingredients are defined on the set of vector functions V X with the domain X…”

Section: Appendixmentioning

confidence: 99%

“…The presence of these uncertainties inhibits the convergence of the conventional estimator to the real state of the system. 1 It is known that this problem in some cases can be solved by sliding mode observers [2][3][4] ; however, in general, the estimation error is never approaching zero under the uncertainties. An alternative approach has been recently developed to solve the last problem.…”

Section: Introductionmentioning

confidence: 99%

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Interval observer design for nonlinear discrete‐time dynamic systems

Zhirabok,

Zuev,

Filaretov

2024

Adaptive Control & Signal

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SummaryThe problem of interval observer design for systems described by nonlinear models with uncertainties is considered. The problem is solved based on special mathematical technique (the algebra of functions) which allows obtaining solution for systems containing non‐smooth nonlinearities. The relations to design interval observer insensitive or having minimal sensitivity to the disturbance and estimating the prescribed nonlinear function of the state vector of the original system are derived. Theoretical results are illustrated by example.

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Section: Appendixmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Interval observer design for nonlinear discrete‐time dynamic systems

Zhirabok,

Zuev,

Filaretov

2024

Adaptive Control & Signal

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“…Besides one assumes that matrix A * is in canonical form. In [24], two different forms are considered: identification and Jordan ones; it was shown that, for the continuous-time systems, the Jordan form is preferable from the point of view of stability. The identification of the canonical form with the matrix…”

Section: Insensitivity To the Disturbancementioning

confidence: 99%

“…has zero eigenvalues, ensuring that the stability is therefore preferable for the discretetime systems. The matrices describing system (12) and model ( 13) meet the following equations based on ( 15) and ( 16) [16,24]:…”

Section: Insensitivity To the Disturbancementioning

confidence: 99%

Virtual Sensors for Nonlinear Discrete-Time Dynamic Systems

et al. 2023

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The problem of virtual sensor design for nonlinear systems under the disturbance is investigated. Two different mathematical techniques are used to solve the problem: the algebra of functions and the logic-dynamic approach. The first one allows obtaining a general solution while the second one produces a solution for nonlinear systems by linear algebra methods. The virtual sensors are designed to be insensitive to the disturbance based on invariant functions. They estimate the prescribed function of the original system state vector. The practical example illustrates theoretical results.

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“…The observer (2) assumes that the matrices A * and C * are in the identification canonical form (ICF): [14] that to design the observer, Jordan canonical form (JCF) of the matrix A * can be used as well:…”

Section: Remarkmentioning

confidence: 99%

Virtual Sensor Design for Replacement the Faulty Physical Sensors

Zhirabok

Zuev

Filaretov

2023

Int. J. Robot. Autom. Technol.

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The paper considers the problem of virtual sensor design for nonlinear dynamic systems with non-smooth nonlinearities described by continuous-time models for faulty physical sensor replacement. It is assumed that to solve the problem, the system is equipped by diagnostic system allowing detecting and isolating the faulty sensor. For every such a sensor, the virtual sensor generating estimate replacing the faulty sensor is designed. To solve the problem, so-called logic-dynamic approach is used which does not guarantee optimal solution but uses only methods of linear algebra to solve the problem for systems with non-smooth nonlinearities. The virtual sensor can be designed in the identification canonical form or Jordan canonical form. The advantage of the first form is a standard procedure of the virtual sensor design while Jordan form allows obtaining a simpler solution. The relations allowing designing the virtual sensor both in identification and in Jordan canonical form are derived.

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Jordan Canonical Form in Diagnosis and Estimation Problems

Cited by 8 publications

References 22 publications

Interval observer design for nonlinear discrete‐time dynamic systems

Interval observer design for nonlinear discrete‐time dynamic systems

Virtual Sensors for Nonlinear Discrete-Time Dynamic Systems

Virtual Sensor Design for Replacement the Faulty Physical Sensors

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