Finite-time stability of linear stochastic fractional-order systems with time delay

Mchiri, Lassaad; Makhlouf, Abdellatif Ben; Băleanu, Dumitru; Rhaima, Mohamed

doi:10.1186/s13662-021-03500-y

Cited by 13 publications

(6 citation statements)

References 23 publications

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“…The FO system is a dynamical system modeled by a fractional differential equation containing derivatives of non-integer order, as shown in Figure 9 [34]. The main feature The active power that producing by SMES can be represented as the following equation:…”

Section: Pid and Fopidmentioning

confidence: 99%

Design and Optimization of Fractional Order PID Controller to Enhance Energy Storage System Contribution for Damping Low-Frequency Oscillation in Power Systems Integrated with High Penetration of Renewable Sources

Abumeteir

Vural

2022

Sustainability

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This paper proposes adding a controller to the energy storage system (ESS) to enhance their contribution for damping low-frequency oscillation (LFO) in power systems integrated with high penetration of different types of renewable energy sources (RES). For instance, wind turbines and photovoltaic (PV) solar systems. This work proposes superconducting magnetic energy storage (SMES) as an ESS. The proportional–integral–derivative (PID) and fractional-order PID (FOPID) are suggested as supporter controllers with SMES. The PID and FOPID controller’s optimal values will be obtained using particle swarm optimization (PSO) is used as the optimization method. Both local area and inter-area oscillation is considered in this work as a LFO. To investigate the impact of adding the SMES with the proposed controller, a multimachine power system with different integration scenarios and cases is carried out with a PV system and wind turbine. The system responses are presented and discussed to show the superiority of the proposed controller both in the time domain and by eigenvalues analysis.

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Section: Pid and Fopidmentioning

confidence: 99%

Design and Optimization of Fractional Order PID Controller to Enhance Energy Storage System Contribution for Damping Low-Frequency Oscillation in Power Systems Integrated with High Penetration of Renewable Sources

Abumeteir

Vural

2022

Sustainability

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“…Since the groundbreaking work of Dorato [24], subsequently, the basic defnition of fnite-time stability in stochastic system was frst proposed by Kushner [25]. Te Grönwall approach was used to establish the fnite-time stability of stochastic fractional system in [26][27][28][29]. Based on the properties of nabla diference for Riemann-Liouvilletype and the generalized Grönwall inequality, Lu et al [26] researched fnite-time stability in the mean for the fractional diference equations with the nabla operator, in which contains uncertain term.…”

Section: Introductionmentioning

confidence: 99%

Novel Results on Finite‐Time Stability of Solutions for Stochastic Ψ‐Hilfer Fractional System

Tian

Luo

2023

Mathematical Problems in Engineering

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This article studies a new kind of Ψ -Hilfer fractional system driven by m -dimensional Brownian motion. By utilizing the generalized Laplace transform and its inverse, the contraction mapping principle, and the properties of a semigroup, we establish the uniqueness of the solution. In addition, finite-time stability is investigated by means of the properties of norm and inequalities scaling technique. As verification, an example is given to show the deduced conclusions.

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“…The FTS of a fractional singular model using a GI method is examined in [18]. The FTS of a stochastic differential model is examined in [19]. A weighted norm method, along with the approach of GI, was utilized to study the FTS bounds of a stochastic differential model in [20].…”

Section: Introductionmentioning

confidence: 99%

Finite-Interval Stability Analysis of Impulsive Fractional-Delay Dynamical System

2023

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Stability analysis over a finite time interval is a well-formulated technique to study the dynamical behaviour of a system. This article provides a novel analysis on the finite-time stability of a fractional-order system using the approach of the delayed-type matrix Mittag-Leffler function. At first, we discuss the solution’s existence and uniqueness for our considered fractional model. Then standard form of integral inequality of Gronwall’s type is used along with the application of the delayed Mittag-Leffler argument to derive the sufficient bounds for the stability of the dynamical system. The analysis of the system is extended and studied with impulsive perturbations. Further, we illustrate the numerical simulations of our analytical study using relevant examples.

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Finite-time stability of linear stochastic fractional-order systems with time delay

Abstract: This paper focuses on the finite-time stability of linear stochastic fractional-order systems with time delay for $\alpha \in (\frac{1}{2},1)$ α ∈ ( 1 2 , 1 ) . Under the generalized Gronwall inequality and stochastic analysis techniques, the finite-time stability of t… Show more

Cited by 13 publications

References 23 publications

Design and Optimization of Fractional Order PID Controller to Enhance Energy Storage System Contribution for Damping Low-Frequency Oscillation in Power Systems Integrated with High Penetration of Renewable Sources

Design and Optimization of Fractional Order PID Controller to Enhance Energy Storage System Contribution for Damping Low-Frequency Oscillation in Power Systems Integrated with High Penetration of Renewable Sources

Novel Results on Finite‐Time Stability of Solutions for Stochastic Ψ‐Hilfer Fractional System

Finite-Interval Stability Analysis of Impulsive Fractional-Delay Dynamical System

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