Functional Observers Design for Linear Systems with Non-commensurate Time Varying Delays

Naami, Ghali; Ouahi, Mohamed; Tissir, El Houssaine; Rabhi, Abdessalem; Ech-charqy, Ahmed

doi:10.1007/s00034-020-01502-x

Cited by 9 publications

(6 citation statements)

References 51 publications

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“…In Figure 4, we trace the functional error e z ( t ) = z ( t ) − z ^ ( t ) , using our approach and the approach presented in Naami et al (2021).…”

Section: Numerical Examplesmentioning

confidence: 99%

Functional observer design for T-S fuzzy neutral systems

Esfouna,

Ouahi,

Tissir

2023

Transactions of the Institute of Measurement and Control

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In this paper, a new fuzzy Functional observer is developed for nonlinear neutral systems. Also, the existence conditions for it are studied. The delay-dependent stability of this observer is guaranteed by the combination of the solution of the Sylvester equation and the Lyapunov–Krasovskii stability approach. The parameters of the studied observer are obtained by solving linear matrix inequalities (LMIs). The performance of the approach developed in this paper is demonstrated at the end of the paper by numerical examples.

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“…In Figure 4, we trace the functional error e z ( t ) = z ( t ) − z ^ ( t ) , using our approach and the approach presented in Naami et al (2021).…”

Section: Numerical Examplesmentioning

confidence: 99%

Functional observer design for T-S fuzzy neutral systems

Esfouna,

Ouahi,

Tissir

2023

Transactions of the Institute of Measurement and Control

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“…Thus, they can be considered as a generalization of these systems (see, for instance, Chaibi et al (2019) and Chaibi et al (2020)). It is also noticed that when the analyses are considered with non-commensurate delay, the results tend to be less conservative (Hua et al, 2021; Naami et al, 2021a; Tissir, 2007).…”

Section: Model Description and Problem Statementmentioning

confidence: 99%

“…De Oliveira and Souza (2020) developed the new enhanced stability criteria for linear systems with multiple time-varying delays. In Naami et al (2021a) and Naami et al (2021b), the design problem of functional observers for linear systems with non-commensurate time-varying delays has been addressed. The problem of controlling of a teleoperation system with a flexible-link slave robot in the presence of time-varying delays, disturbances, actuator defects, and input saturation was suggested in Rasouli et al (2021).…”

Section: Introductionmentioning

confidence: 99%

Delay-dependent H_∞ dynamic observers for non-linear systems with multiple time-varying delays

Naami

Ouahi

Sadek

et al. 2022

Transactions of the Institute of Measurement and Control

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The design of dynamic [Formula: see text] observers (DO) for non-linear Lipschitz systems with multiple time-varying delays and disturbances is studied. Sufficient conditions for the existence of these observers are presented in the form of rank equality. Compared to previously published work, the system under consideration includes non-linearity, non-commensurable delay, and external disturbance. Through the use of the Wirtinger inequality and the extended reciprocally convex matrix inequality, new and less conservative delay-dependent conditions in terms of linear matrix inequalities (LMIs) are derived based on the Lyapunov–Krasovskii functional method. Solving these LMIs makes it possible to obtain DO that satisfies an [Formula: see text] performance index. Through two numerical examples in which the comparison with the proportional observer (PO) and the proportional–integral observer (PIO) shows the efficiency of the proposed DO synthesis condition. Furthermore, the results indicate that the DO developed in this paper is more resilient to parameter perturbations.

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“…Over the past three decades, considerable effort has been devoted to the synthesis of time-delay systems, leading to numerous research results for both continuous-time and discrete-time systems. [1][2][3][4][5][6][7][8][9][10] Understanding and analyzing the impact of delays requires the development of stability criteria. Lyapunov stability theory and linear matrix inequality (LMI) technology have been widely used in most studies concerning the stability of time-delay systems.…”

Section: Introductionmentioning

confidence: 99%

“…Time‐varying delay (TVD) is a well‐known challenge in engineering applications, often leading to poor system performance, instability, and failure to achieve desired objectives. Over the past three decades, considerable effort has been devoted to the synthesis of time‐delay systems, leading to numerous research results for both continuous‐time and discrete‐time systems 1‐10 …”

Section: Introductionmentioning

confidence: 99%

H_∞ dynamic observer design for a class of Lipschitz nonlinear discrete‐time systems with time varying delays

Naami,

Ouahi

2023

Optim Control Appl Methods

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This study explores the development of dynamic observer (HDO) for discrete‐time nonlinear systems (DTNLS) with time‐varying delay (TVD) and disturbances. The approach is to construct an augmented Lyapunov–Krasovskii function (LKF) with double summation terms, using the generalized reciprocally convex matrix inequality (GRCMI), as well as the Jensen‐based inequality (JBI) and the Wirtinger‐based inequality (WBI). These lead to less conservative time‐dependent conditions, represented as a set of linear matrix inequalities (LMIs) that can be efficiently solved using the LMI or YALMIP toolboxes. In addition, the proposed observer includes the widely used proportional observer (PO) and proportional integral observer (PIO) as specific cases. Two examples are presented to demonstrate the validity and effectiveness of the results.

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Functional Observers Design for Linear Systems with Non-commensurate Time Varying Delays

Cited by 9 publications

References 51 publications

Functional observer design for T-S fuzzy neutral systems

Functional observer design for T-S fuzzy neutral systems

Delay-dependent H_∞ dynamic observers for non-linear systems with multiple time-varying delays

H_∞ dynamic observer design for a class of Lipschitz nonlinear discrete‐time systems with time varying delays

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Functional Observers Design for Linear Systems with Non-commensurate Time Varying Delays

Cited by 9 publications

References 51 publications

Functional observer design for T-S fuzzy neutral systems

Functional observer design for T-S fuzzy neutral systems

Delay-dependent H∞ dynamic observers for non-linear systems with multiple time-varying delays

H∞ dynamic observer design for a class of Lipschitz nonlinear discrete‐time systems with time varying delays

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Delay-dependent H_∞ dynamic observers for non-linear systems with multiple time-varying delays

H_∞ dynamic observer design for a class of Lipschitz nonlinear discrete‐time systems with time varying delays