Robust stability of fractional-order systems with mixed uncertainties: The <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg" display="inline" id="d1e518"><mml:mrow><mml:mn>0</mml:mn><mml:mo linebreak="goodbreak" linebreakstyle="after">&lt;</mml:mo><mml:mi>α</mml:mi><mml:mo linebreak="goodbreak" linebreakstyle="after">&lt;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> case

Zhang, Qing-Hao; Lu, Jun-Guo

doi:10.1016/j.cnsns.2023.107511

Communications in Nonlinear Science and Numerical Simulation

2023

DOI: 10.1016/j.cnsns.2023.107511

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Robust stability of fractional-order systems with mixed uncertainties: The 0<α<1 case

Qing-Hao Zhang,

Jun-Guo Lu

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2024

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Cited by 6 publications

References 46 publications

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Controllability, observability, and stability of φ‐conformable fractional linear dynamical systems

Sadek

2024

Asian Journal of Control

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This paper focuses on two main aspects. Firstly, we introduce a generalized form of conformable fractional derivatives called ‐conformable fractional derivatives along with their corresponding integrals . We also present several theorems related to these derivatives. Secondly, we investigate the observability, controllability, and stability of a fractional dynamical system known as the ‐conformable fractional dynamical system ( ‐CF‐DS). We establish the connection between controllability, the controllability matrix, and the fractional ‐conformable fractional differential Lyapunov equation ( ‐CF‐DLE). We prove that the ‐CF‐DS is stable if and only if all eigenvalues of the matrix have negative real parts. Moreover, we provide theorems regarding the observability of an ‐CF‐DS. To demonstrate the efficacy of our results, we include illustrative examples.

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Controllability, observability, and stability of φ‐conformable fractional linear dynamical systems

Sadek

2024

Asian Journal of Control

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Robust stability and stabilization of continuous‐discrete fractional‐order 2D Fornasini–Marchesini second model with interval uncertainties

Zhu,

2024

Asian Journal of Control

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This paper investigates the robust stability and stabilization problems of continuous‐discrete fractional‐order two‐dimensional Fornasini–Marchesini second model with interval uncertainties. Firstly, for the nominal model with fractional‐order , the unified LMI‐based stability conditions are presented by general description of stable root‐clustering sets. Secondly, these stability conditions are transformed to be more tractable for stabilization, and the LMI/BMI‐based stabilization conditions are established via state feedback controllers. Meanwhile, one algorithm is proposed to solve the BMI‐based conditions. Thirdly, facing interval uncertainties in this model, the LMI‐based robust stability conditions and LMI/BMI‐based robust stabilization conditions are established. Lastly, two examples are given to show the validity of our robust stability and stabilization results.

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Robust asymptotic stability analysis for fractional-order systems with commensurate time delays: The 1 < β ≤ 2 case

Zhang,

Lu,

Zhang

2024

Applied Mathematics and Computation

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Robust stability of fractional-order systems with mixed uncertainties: The 0<α<1 case

Cited by 6 publications

References 46 publications

Controllability, observability, and stability of φ‐conformable fractional linear dynamical systems

Controllability, observability, and stability of φ‐conformable fractional linear dynamical systems

Robust stability and stabilization of continuous‐discrete fractional‐order 2D Fornasini–Marchesini second model with interval uncertainties

Robust asymptotic stability analysis for fractional-order systems with commensurate time delays: The 1 < β ≤ 2 case

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Robust stability of fractional-order systems with mixed uncertainties: The 0<α<1 case

Cited by 6 publications

References 46 publications

Controllability, observability, and stability of φ‐conformable fractional linear dynamical systems

Controllability, observability, and stability of φ‐conformable fractional linear dynamical systems

Robust stability and stabilization of continuous‐discrete fractional‐order 2D Fornasini–Marchesini second model with interval uncertainties

Robust asymptotic stability analysis for fractional-order systems with commensurate time delays: The 1 < β ≤ 2 case

Contact Info

Product

Resources

About

Robust asymptotic stability analysis for fractional-order systems with commensurate time delays: The 1 < β ≤ 2 case