Robust $H_{\infty }$ Observer-Based Control of Fractional-Order Systems With Gain Parametrization

Boukal, Yassine; Darouach, Mohamed; Zasadzinski, Michel; Radhy, Nour-Eddine

doi:10.1109/tac.2017.2690140

Cited by 56 publications

(24 citation statements)

References 35 publications

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“…Based on Definition 2, the augmented estimation error system (9) in the presence of the AETS is robust mean-square stable, which means that the estimator (7) can achieve the state estimation of the fractional-order nonlinear uncertain system (1). The proof is completed.…”

Section: Resultsmentioning

confidence: 90%

“…In the following, two theorems are investigated for the synthetic analysis of the fractional-order augmented estimation error system (9) subject to the AETS. Theorem 1 derives a sufficient condition for the robust mean-square stability of the estimation error system (9). Based on the result in Theorem 1, Theorem 2 proposes a LMI-based design method for the state estimator (7) in the presence of the adaptive event-triggered transmission scheme.…”

Section: Resultsmentioning

confidence: 99%

“…Based on the result in Theorem 1, Theorem 2 proposes a LMI-based design method for the state estimator (7) in the presence of the adaptive event-triggered transmission scheme. Theorem 1: For some given scalars η 1 > 0, η 2 > 0, γ > 0 and estimator gainsÂ, L, the fractional-order augmented estimation error system (9) under the AETS is robust mean-square stable, if there exists a matrix P = diag{P 1 , P 2 } > 0, such that the following matrix inequality holds.…”

Section: Resultsmentioning

confidence: 99%

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Robust State Estimation for Fractional-Order Nonlinear Uncertain Systems via Adaptive Event-Triggered Communication Scheme

Xiong

Tan

2019

IEEE Access

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This paper is concerned with the adaptive event-triggered robust state estimation for a class of fractional-order nonlinear uncertain systems, where the fractional order satisfies 0 < α < 1. To save bandwidth resources effectively, an adaptive event-triggered scheme (AETS) is proposed to judge whether the measurement output of the sensor needs to be released to the estimator or not. Firstly, by taking the AETS into consideration, a novel fractional-order estimation error model is established. Then, based on this system model, a sufficient condition that can ensure the robust mean-square stability of the estimation error system has been derived by utilizing the Lyapunov functional approach and some properties of Mittag-Leffler functions. Meanwhile, by applying matrix's singular value decomposition (SVD) technique, the design of the state estimator has been solved in terms of solving the solution of linear matrix inequality (LMI). Finally, one provides a numerical example to verify the feasibility of the proposed method. INDEX TERMS Fractional-order nonlinear uncertain system, robust state estimation, adaptive event-triggered scheme.

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Section: Resultsmentioning

confidence: 90%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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Robust State Estimation for Fractional-Order Nonlinear Uncertain Systems via Adaptive Event-Triggered Communication Scheme

Xiong

Tan

2019

IEEE Access

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“…In the work of Boukal et al, 41 the LMI conditions are proposed to achieve a suitable feedback gain K and observer gain Z such that inequality (44) holds. However, using the mentioned method in the aforementioned work, 41 the gains L and K are obtained in one step and their calculations depend to each other. In the following, we propose a new method such that the gains L and K can be found in two separate steps without dependence on each other.…”

Section: Observer-based Stabilizationmentioning

confidence: 99%

Fractional‐order–dependent global stability analysis and observer‐based synthesis for a class of nonlinear fractional‐order systems

Tavazoei

Asemani

2018

Intl J Robust & Nonlinear

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This paper focuses on proposing novel conditions for stability analysis and stabilization of the class of nonlinear fractional-order systems. First, by considering the class of nonlinear fractional-order systems as a feedback interconnection system and applying small-gain theorem, a condition is proposed for L 2 -norm boundedness of the solutions of these systems. Then, by using the Mittag-Leffler function properties, we show that satisfaction of the proposed condition proves the global asymptotic stability of the class of nonlinear fractional-order systems with fractional order lying in (0.5, 1) or (1.5, 2). Unlike the Lyapunov-based methods for stability analysis of fractional-order systems, the new condition depends on the fractional order of the system. Moreover, it is related to the H ∞ -norm of the linear part of the system and it can be transformed to linear matrix inequalities (LMIs) using fractional-order bounded-real lemma. Furthermore, the proposed stability analysis method is extended to the state-feedback and observer-based controller design for the class of nonlinear fractional-order systems based on solving some LMIs. In the observer-based stabilization problem, we prove that the separation principle holds using our method and one can find the observer gain and pseudostate-feedback gain in two separate steps. Finally, three numerical examples are provided to demonstrate the advantage of the novel proposed conditions with the previous results. KEYWORDSH ∞ -norm, nonlinear control, nonlinear fractional-order system, observer-based stabilization, pseudostate feedback Int J Robust Nonlinear Control. 2018;28:4549-4564. wileyonlinelibrary.com/journal/rnc

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“…Chen et al [19] studied the global Mittag-Leffler projective synchronization for nonidentical fractional-order neural networks with a time delay by designing a delayed sliding mode controller to ensure the occurrence of the sliding motion. There are many related results reported in various books and review articles [20][21][22][23][24][25][26]. Xie et al [26] presented a numerical scheme for the coupled systems of fractional-order integral-differential equations based on the Haar wavelet.…”

Section: Introductionmentioning

confidence: 99%

Global Mittag-Leffler stability for fractional-order coupled systems on network without strong connectedness

Meng

Kao

Karimi

et al. 2020

Sci. China Inf. Sci.

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This study investigates the global Mittag-Leffler stability (MLS) problem of the equilibrium point for a new fractional-order coupled system (FOCS) on a network without strong connectedness. In particular, an integer-order coupled system is extended into the FOCS on a complex network without strong connectedness. Based on the theory of asymptotically autonomous systems and graph theory, sufficient conditions are derived to ensure the existence, uniqueness, and global MLS of the solutions of this FOCS on a network. Finally, a numerical example is provided to demonstrate the validity and potential of the proposed method for studying the MLS of FOCSs.

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Robust $H_{\infty }$ Observer-Based Control of Fractional-Order Systems With Gain Parametrization

Cited by 56 publications

References 35 publications

Robust State Estimation for Fractional-Order Nonlinear Uncertain Systems via Adaptive Event-Triggered Communication Scheme

Robust State Estimation for Fractional-Order Nonlinear Uncertain Systems via Adaptive Event-Triggered Communication Scheme

Fractional‐order–dependent global stability analysis and observer‐based synthesis for a class of nonlinear fractional‐order systems

Global Mittag-Leffler stability for fractional-order coupled systems on network without strong connectedness

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