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Reachability and Controllability of Fractional Singular Dynamical Systems with Control Delay

Author

Listed:
  • Hai Zhang
  • Jinde Cao
  • Wei Jiang

Abstract

This paper is concerned with the reachability and controllability of fractional singular dynamical systems with control delay. The factors of such systems including the Caputo’s fractional derivative, control delay, and singular coefficient matrix are taken into account synchronously. The state structure of fractional singular dynamical systems with control delay is characterized by analysing the state response and reachable set. A set of sufficient and necessary conditions of controllability for such systems are established based on the algebraic approach. Moreover, an example is provided to illustrate the effectiveness and applicability of the proposed criteria.

Suggested Citation

  • Hai Zhang & Jinde Cao & Wei Jiang, 2013. "Reachability and Controllability of Fractional Singular Dynamical Systems with Control Delay," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:567089
    DOI: 10.1155/2013/567089
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    References listed on IDEAS

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    1. R. Ganesh & R. Sakthivel & N. I. Mahmudov & S. M. Anthoni, 2013. "Approximate Controllability of Fractional Integrodifferential Evolution Equations," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, May.
    2. Raúl Manzanilla & Luis Gerardo Mármol & Carmen J. Vanegas, 2010. "On the Controllability of a Differential Equation with Delayed and Advanced Arguments," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-16, July.
    3. R. Ganesh & R. Sakthivel & N. I. Mahmudov & S. M. Anthoni, 2013. "Approximate Controllability of Fractional Integrodifferential Evolution Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    4. Hai Zhang & Jinde Cao & Wei Jiang, 2013. "Controllability Criteria for Linear Fractional Differential Systems with State Delay and Impulses," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-9, June.
    5. Hai Zhang & Jinde Cao & Wei Jiang, 2013. "Controllability Criteria for Linear Fractional Differential Systems with State Delay and Impulses," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    6. Raúl Manzanilla & Luis Gerardo Mármol & Carmen J. Vanegas, 2010. "On the Controllability of a Differential Equation with Delayed and Advanced Arguments," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
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    Citations

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    Cited by:

    1. Hai Zhang & Daiyong Wu & Jinde Cao, 2014. "Asymptotic Stability of Caputo Type Fractional Neutral Dynamical Systems with Multiple Discrete Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Ma, Weiyuan & Ma, Chenjun & Wang, Xiaoqin & Sun, Weigang, 2025. "Delayed control-based controllability of discrete fractional higher-order neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 200(P1).

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