Singularly Perturbed Problems with Multi-Tempo Fast Variables

Курина, Г. А.; Kalashnikova, Margarita

doi:10.1134/s00051179220110017

Cited by 8 publications

(2 citation statements)

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“…, where S f (t) and S 0 f (t) are the observability matrices of the tfamily of fast subsystems and its canonical Frobenius form, calculated using the formulas ( 12), (13) with matrices A 4 (t), c 2 (t) and A 0 f (t), c 0 f (t), respectively. 3) Choose real numbers λ 1 , λ 2 , .…”

Section: Observers For Subsystemsmentioning

confidence: 99%

“…as models of multi-tempo processes when simulating the dynamics of aircraft, chemical reactions, movements of robotic manipulators, etc. (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].…”

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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Section: Observers For Subsystemsmentioning

confidence: 99%