New Results on Stabilization of Fractional‐Order Nonlinear Systems via an LMI Approach

Thuận, Mai Viết; Huong, Dinh Cong

doi:10.1002/asjc.1644

Cited by 33 publications

(33 citation statements)

References 46 publications

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“…The utilization of linear matrix inequality (LMI)-based methods has been increased by the evolution of efficient numerical procedures to solve convex optimization problems [20][21][22][23][24][25][26] defined by LMI conditions. Appropriate LMI conditions for asymptotic stability analysis of FO-LTI systems with fractional orders in and intervals are presented in [27] and [28], respectively.…”

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confidence: 99%

Stability and Stabilization of Fractional‐Order Systems with Different Derivative Orders: An LMI Approach

Badri

Sojoodi

2018

Asian Journal of Control

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Stability and stabilization analysis of fractional‐order linear time‐invariant (FO‐LTI) systems with different derivative orders is studied in this paper. First, by using an appropriate linear matrix function, a single‐order equivalent system for the given different‐order system is introduced by which a new stability condition is obtained that is easier to check in practice than the conditions known up to now. Then the stabilization problem of fractional‐order linear systems with different fractional orders via a dynamic output feedback controller with a predetermined order is investigated, utilizing the proposed stability criterion. The proposed stability and stabilization theorems are applicable to FO‐LTI systems with different fractional orders in one or both of 0 < α < 1 and 1 ≤ α < 2 intervals. Finally, some numerical examples are presented to confirm the obtained analytical results.

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confidence: 99%

Stability and Stabilization of Fractional‐Order Systems with Different Derivative Orders: An LMI Approach

Badri

Sojoodi

2018

Asian Journal of Control

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“…Remark In [29], the authors used the Lyapunov direct method [20] to prove the Mittag‐Leffler stability of fractional order system with time‐varying structured uncertainties. Here, we use the fractional type Halanay inequality [26] to obtain the asymptotic stability result of fractional order system with time‐varying structured uncertainties and time delay.…”

Section: Resultsmentioning

confidence: 99%

Stabilization of uncertain fractional order system with time‐varying delay using BMI approach

Zhou

Kou

et al. 2019

Asian Journal of Control

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This paper considers the systematic design of robust stabilizing state feedback controllers for fractional order nonlinear systems with time‐varying delay being possibly unbounded. By using the fractional Halanay inequality and the Caputo fractional derivative of a quadratic function, stabilizability conditions expressed in terms of bilinear matrix inequalities are derived. The controllers can then be obtained by computing the gain matrices. In order to derive the gain matrices, two algorithms are proposed by using the existing computationally linear matrix inequality techniques. Two numerical examples with simulation results are provided to demonstrate the effectiveness of the obtained results.

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“…Compared with an integer-order dynamical model, fractional-order dynamical model is more accurate, nonlocal, and has weakly singular kernels but integer-order dynamical behavior fails in this aspect. [28][29][30][31][32][33][34] So, dynamical behavior of the fractional-order systems based on fractional-order calculation is very significant, and some excellent results have been demonstrated. [35][36][37] The further study of fractional derivatives is needed to an essential issue of its widespread application in the stability, stabilization, Chao's synchronization, control theory, etc.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis and robust synchronization of fractional‐order competitive neural networks with different time scales and impulsive perturbations

Anbalagan

Raja

Agarwal

et al. 2019

Adaptive Control & Signal

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This article mainly examine a class of robust synchronization, global stability criterion, and boundedness analysis for delayed fractional-order competitive type-neural networks with impulsive effects and different time scales. Firstly, by endowing the robust analysis skills and a new class of Lyapunov-Krasovskii functional approach, the error dynamical system is furnished to be a robust adaptive synchronization in the voice of linear matrix inequality (LMI) technique. Secondly, by ignoring the uncertain parameter terms, the existence of equilibrium points are established by means of topological degree properties, and the solution representation of the considered network model are provided. Thirdly, a novel global asymptotic stability condition is proposed in the voice of LMIs, which is less conservative. Finally, our analytical results are justified with two numerical examples with simulations.

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New Results on Stabilization of Fractional‐Order Nonlinear Systems via an LMI Approach

Cited by 33 publications

References 46 publications

Stability and Stabilization of Fractional‐Order Systems with Different Derivative Orders: An LMI Approach

Stability and Stabilization of Fractional‐Order Systems with Different Derivative Orders: An LMI Approach

Stabilization of uncertain fractional order system with time‐varying delay using BMI approach

Stability analysis and robust synchronization of fractional‐order competitive neural networks with different time scales and impulsive perturbations

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