Robust finite-time control of fractional-order nonlinear systems via frequency distributed model

Wang, Bin; Ding, Junling; Wu, Faqi; Zhu, Daqi

doi:10.1007/s11071-016-2819-9

Cited by 48 publications

(38 citation statements)

References 37 publications

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“…Condition (20) shows that (MM 3 /αω)L < 1, which implies that Q is a contraction. Hence, we deduce by the principle of Banach contraction that Q has a unique fixed point, which is the unique solution to equation (9). e proof is completed.…”

Section: Theoremmentioning

confidence: 74%

“…Similar to eorem 1, we now prove the stability of equation 9 en, the zero solution of system (9) is locally asymptotically stable, if the following conditions are satisfied:…”

Section: Theoremmentioning

confidence: 94%

“…where M, M 3 , and ω are constants appeared in (13) and (8), then equation (9), with the initial condition x(0) � x 0 and x′(0) � x 1 , has a unique solution in [0, T].…”

Section: Theoremmentioning

confidence: 99%

“…ere has been more literature on stability of dynamic fractional-order systems, in which important and sufficient conditions were discussed for the stability of linear and linear time-delay fractional differential equations as stated in [8][9][10]. e modelling and stability of the water jet mixed-flow pump fractional-order shafting system has also been studied [11].…”

Section: Introductionmentioning

confidence: 99%

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Stability and Stabilization for a Class of Semilinear Fractional Differential Systems

Ibrahim

Dong

Zhang

2020

Journal of Function Spaces

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This paper considers a class of semilinear fractional-order systems with Caputo derivative. New conditions ensuring asymptotic stability and stabilization of fractional systems with the fractional order between 0 and 2 are proposed. The analysis is based on a property of convolution and asymptotic properties of Mittag-Leffler functions. Some numerical examples are provided to illustrate the feasibility and validity of the proposed approach.

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Section: Theoremmentioning

confidence: 74%

“…Similar to eorem 1, we now prove the stability of equation 9 en, the zero solution of system (9) is locally asymptotically stable, if the following conditions are satisfied:…”

Section: Theoremmentioning

confidence: 94%

“…where M, M 3 , and ω are constants appeared in (13) and (8), then equation (9), with the initial condition x(0) � x 0 and x′(0) � x 1 , has a unique solution in [0, T].…”

Section: Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stability and Stabilization for a Class of Semilinear Fractional Differential Systems

Ibrahim

Dong

Zhang

2020

Journal of Function Spaces

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“…(4) contains integer-order derivative terms which formulate the fractionalorder differential equations with clear physical interpretations. Moreover, the Caputo fractional-order derivative has the widely spread application in the actual modeling process [35]. Hence, the Caputo definition is considered in this paper to characterize the genetic memory properties of energy saving, carbon emissions, GDP, and renewable energy development.…”

Section: Property 1 ([35])mentioning

confidence: 99%

Fractional-order modeling and sliding mode control of energy-saving and emission-reduction dynamic evolution system

Huang

Zhou

et al. 2018

International Journal of Electrical Power & Energy Systems

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A B S T R A C TThis paper proposes the fractional-order modeling for sliding mode control of a complex four-dimensional energy-saving and emission-reduction system (ESERS). In the proposed methodology, the fractional calculus techniques are employed to accurately model the dynamics of the ESERS, and the fractional-order model of the energy-saving and emission-reduction system (FOESERS) is formulated. With the proposed FOESERS, all of the equilibrium points and the corresponding eigenvalues are obtained, and the instability region and the state trajectories of FOESERS are also given. The FOESERS can represent complex dynamic behaviours with chaotic and unstable states on the energy conservation, carbon emissions, economic growth, and renewable energy development, and have a great impact on the formulation of government energy policies. Furthermore, based on the fractional Lyapunov stability and robust control theory, a sliding-mode controller is designed to control the FOESERS with model uncertainties and external disturbances to the equilibrium point in the finite time. Finally, simulation results confirm the effectiveness and robustness of the proposed scheme.

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Analysis of Bifurcation Characteristics of Fractional‐Order Direct Drive Permanent Magnet Synchronous Generator

Chen,

Kou,

Wei

et al. 2024

Energy Science & Engineering

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In this study, we establish a fractional‐order direct drive permanent magnet synchronous wind turbines (DPMSG) model defined by Caputo based on the fractional calculus theory to overcome the singularity and limitations of integer‐order DPMSG models. The path and characteristics of the DPMSG system entering the bifurcation and chaos caused by the internal parameter changes and external disturbances were analyzed. First, we established a nonlinear fractional‐order mathematical model of a DPMSG system. Second, a bifurcation diagram was drawn using the maximum algorithm, and the path to chaos of the system at different orders was analyzed by combining its chaotic phase portrait and temporal sequence diagram. Subsequently, the impact of variations in the system order on the chaotic features of the original system was analyzed. The internal parameter adjustments of the system and changes in the system stability under external disturbances and other external excitations were analyzed. The influence of the system on its bifurcation phenomenon and chaotic behavior under multidimensional orders was determined, and it was observed that its path into chaos was opened by period‐doubling bifurcation. Lastly, the dual‐parameter stability domain of the system order corresponding to the internal parameters of the system was obtained by determining the parameter conditions for the critical stability of the system.

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Robust finite-time control of fractional-order nonlinear systems via frequency distributed model

Cited by 48 publications

References 37 publications

Stability and Stabilization for a Class of Semilinear Fractional Differential Systems

Stability and Stabilization for a Class of Semilinear Fractional Differential Systems

Fractional-order modeling and sliding mode control of energy-saving and emission-reduction dynamic evolution system

Analysis of Bifurcation Characteristics of Fractional‐Order Direct Drive Permanent Magnet Synchronous Generator

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