Finite‐time functional interval observer for linear systems with uncertainties

Liu, Long-Wen; Xie, Wei; Khan, Awais Gul; Zhang, Lang-wen

doi:10.1049/iet-cta.2020.0200

Cited by 11 publications

(9 citation statements)

References 37 publications

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“…Such an assumption is usually taken into account when some sub-model is designed. 25,27,31,32 As is shown in References 31 and 32, the function 𝜑 satisfies the condition…”

Section: Sub-model Designmentioning

confidence: 86%

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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“…Such an assumption is usually taken into account when some sub-model is designed. 25,27,31,32 As is shown in References 31 and 32, the function 𝜑 satisfies the condition…”

Section: Sub-model Designmentioning

confidence: 86%

Interval observer design for nonlinear discrete‐time dynamic systems

Zhirabok,

Zuev,

Filaretov

2024

Adaptive Control & Signal

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“…Proposition 2 (Liu et al 32 ). For any pair of polynomials 𝒜 (s) ∈ R n×n [s] and ℬ(s) ∈ R p×n [s], there exists…”

Section: R-io Solution and Optimizationmentioning

confidence: 98%

“…Input A, B, C, y(t), u(t), 𝜐(t), 𝜐(t), 𝜔(t), 𝜔(t), x(t 0 ), and x(t 0 ); Output x(t) and x(t); 32) to obtain 𝒫 (s), ℛ(s), and 𝒬 1 (s);…”

Section: Algorithm 1 Optimal R-io Design Technique Of Uncertain Systemmentioning

confidence: 99%

Optimal reduced‐order interval observer design for uncertain continuous‐time linear systems

Liu

Xie

Zhang

2022

Intl J Robust & Nonlinear

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This article investigates the reduced‐order interval observer (R‐IO) design technique for continuous‐time linear systems with unknown external disturbances and measurement noises. First, we propose a coupled R‐IO structure with more design degrees of freedom, and it can be directly applied not only to solve the difficulty of the error system cooperativity construction but to relax the constraint on the sensor measurement noises. Second, the R‐IO existence condition is derived as a set of matrix equations (MEs), and a complete solution, explicitly showing the available design parameters, to such an R‐IO is further obtained by solving the MEs. Third, using the solution, an integrated optimization indicator of the R‐IO performance is built as the valid selection mechanism of these parameters. Finally, the efficiency of the obtained results is illustrated through a numerical example and a practical example.

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“…Inspired by the above two references, this study presents a solution to the FIO design problem of the LTV system using the parametric design technique. Different from traditional methods, parametric design directly provides all control laws within the system framework, including the freedom parameters, and modifying the free parameters can correspond to changes in the design requirements (Gu et al, 2022c(Gu et al, , 2021bGu and Wang, 2022;Liu et al, 2020Liu et al, , 2022.…”

Section: Introductionmentioning

confidence: 99%

Functional interval observer design for linear time-varying systems with additive disturbances

Sun

Liu

2022

Transactions of the Institute of Measurement and Control

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This paper investigates the problem of the functional interval observer design for linear time-varying (LTV) systems with additive disturbances in both input and output channels. First, sufficient conditions for the existence of a functional interval observer for LTV systems are proposed. Based on the solution of a type of Sylvester matrix equations (generalized Sylvester equations, GSEs), completely parameterized expressions of functional interval observer coefficient matrices are established, yielding a simple and effective design approach for solving the interval estimation issue of the LTV system, while the free parameters in the expressions provide the design degrees of freedom that can be utilized to achieve additional system specifications. Furthermore, the developed observer may execute state estimation at the desired convergence rate, considerably improving estimate performance. Finally, a numerical example and a back-to-turn (BTT) aircraft control example are presented, with the results showing that the upper and lower bounds provided by the designed observer provide a better performance of interval estimation of the functional state variables, demonstrating the effectiveness of the proposed method.

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Finite‐time functional interval observer for linear systems with uncertainties

Cited by 11 publications

References 37 publications

Interval observer design for nonlinear discrete‐time dynamic systems

Interval observer design for nonlinear discrete‐time dynamic systems

Optimal reduced‐order interval observer design for uncertain continuous‐time linear systems

Functional interval observer design for linear time-varying systems with additive disturbances

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