Sufficient and Necessary Condition of Admissibility for Fractional-order Singular System

Yu, Yanxin; Jiao, Zhuang; Sun, Changyin

doi:10.1016/s1874-1029(14)60003-3

Cited by 53 publications

(44 citation statements)

References 23 publications

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“…Moreover, due to uniqueness and existence of the theorem for fractional order singular system, [29] Proof: The proof follows from the proof of Theorem 1. Namely, from (49), (50) one can easily find that ( ) …”

Section: Convergence Analysismentioning

confidence: 98%

“…denotes the α th-order Caputo fractional derivative with respect to t, while , E A, and C are matrices with appropriate dimensions [28,29]. In solving a singular problem, assuming regularity of the system, it is necessary to ensure the existence and uniqueness of the solution.…”

Section: Fractional-order Autonomous Linear Singular Systemmentioning

confidence: 99%

“…Also, the initial conditions of fractional differential equations which were compared to the given fractional derivatives were considered by different authors [29,31], assuming that there was no difficulty regarding the questions of existence, uniqueness, and continuity of solutions with respect to initial data. The following assumptions on the system (16), (17) …”

Section: Closed-loop Fractional-order Iterative Learning Controlmentioning

confidence: 99%

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Fractional-order iterative learning control for singular fractional- order system: (P) - PDa type

Lazarević¹,

Djurovic²,

Cvetković³

et al. 2016

Sci Tech Rev

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Iterative learning control (ILC) is one of the recent topics in control theories and it is suitable for controlling a wider class of mechatronic systems -it is especially suitable for the motion control of robotic systems. This paper addresses the problem of application of fractional order ILC for fractional order singular system. Particularly, we study fractional order singular systems in the pseudo-state space. An closed-loop fractional order PDalpha type ILC of the fractional-order singular system is investigated. Also, open-closed loop of the fractional order P-PDa type ILC is considered. Sufficient conditions for the convergence in the time domain of the proposed ILC schemes are given by the corresponding theorems and proved. Finally, numerical simulations show the feasibility and effectiveness of the proposed approach.

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Section: Convergence Analysismentioning

confidence: 98%

Section: Fractional-order Autonomous Linear Singular Systemmentioning

confidence: 99%

Section: Closed-loop Fractional-order Iterative Learning Controlmentioning

confidence: 99%

See 1 more Smart Citation

Fractional-order iterative learning control for singular fractional- order system: (P) - PDa type

Lazarević¹,

Djurovic²,

Cvetković³

et al. 2016

Sci Tech Rev

View full text Add to dashboard Cite

show abstract

“…By developing Δ ( ), Δ ( ), and Δ ( ), according to (7), (16), and applying Lemma 7 to inequality (33) for any real scalar 2 > 0, we have…”

Section: ψ ( ( )) ψ ( ( )) = [φ (̂( )) (φ ( ( )) − φ (̂( ))) ] [ φ (̂mentioning

confidence: 99%

“…The finite-dimensional fractionalorder state-space model with the zero initial conditions was equivalent to an infinite-dimensional integer-order statespace model and two specific types of Lyapunov candidate functions were proposed to investigate the stability problem of fractional differential equations (FDEs) in [14]. The stability conditions of singular FOS and fractional-order delay system are given in [15][16][17][18][19]. Recently, [20,21] provides a good survey of the methods available to analyze the stability of fractional-order differential systems, the reader may refer to them and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Observer‐Based Robust Controller Design for Nonlinear Fractional‐Order Uncertain Systems via LMI

Qiu

2017

Mathematical Problems in Engineering

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We discuss the observer-based robust controller design problem for a class of nonlinear fractional-order uncertain systems with admissible time-variant uncertainty in the case of the fractional-order satisfying 0 < < 1. Based on direct Lyapunov approach, a sufficient condition for the robust asymptotic stability of the observer-based nonlinear fractional-order uncertain systems is presented. Employing Finsler's Lemma, the systematic robust stabilization design algorithm is then proposed in terms of linear matrix inequalities (LMIs). The efficiency and advantage of the proposed algorithm are finally illustrated by two numerical simulations.

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Necessary and sufficient admissibility conditions of dynamic output feedback for singular linear fractional‐order systems

Marir

Chadli

Basin

2022

Asian Journal of Control

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This paper studies the stabilization problem for linear continuous‐time singular fractional‐order systems with the fractional‐order α$$ \alpha $$ satisfying 1<α<2$$ 1<\alpha <2 $$. New formulations of the admissibility for the closed‐loop system by dynamic output feedback controller are obtained using necessary and sufficient scriptLscriptMscriptI$$ \mathcal{LMI} $$ (linear matrix inequality) conditions, to generalize existing results in the literature for integer‐order systems. The derived results are validated by numerical examples demonstrating applicability and efficacy of the presented approach.

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Sufficient and Necessary Condition of Admissibility for Fractional-order Singular System

Cited by 53 publications

References 23 publications

Fractional-order iterative learning control for singular fractional- order system: (P) - PDa type

Fractional-order iterative learning control for singular fractional- order system: (P) - PDa type

Observer‐Based Robust Controller Design for Nonlinear Fractional‐Order Uncertain Systems via LMI

Necessary and sufficient admissibility conditions of dynamic output feedback for singular linear fractional‐order systems

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