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Controllability Criteria for Linear Fractional Differential Systems with State Delay and Impulses

Author

Listed:
  • Hai Zhang
  • Jinde Cao
  • Wei Jiang

Abstract

This paper is concerned with the controllability of linear fractional differential systems with delay in state and impulses. The factors of such systems including fractional derivative, impulses, and delay are taken into account synchronously. The expression of state response for such systems is derived, and the sufficient and necessary conditions of controllability criteria are established. Both the proposed criteria and illustrative examples show that the controllability property of the linear systems is dependent neither on the order of fractional derivative, on delay nor on impulses.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:146010
    DOI: 10.1155/2013/146010
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    References listed on IDEAS

    as
    1. Hong Shi & Guangming Xie, 2012. "Controllability and Observability Criteria for Linear Piecewise Constant Impulsive Systems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. N. I. Mahmudov, 2013. "Approximate Controllability of Fractional Sobolev‐Type Evolution Equations in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. 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.
    4. Rabha W. Ibrahim, 2012. "Complex Transforms for Systems of Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    5. Jinhua Wang & Hongjun Xiang, 2010. "Upper and Lower Solutions Method for a Class of Singular Fractional Boundary Value Problems with p‐Laplacian Operator," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    6. Shinn-Horng Chen & Wen-Hsien Ho & Jyh-Horng Chou, 2012. "Robust Local Regularity and Controllability of Uncertain TS Fuzzy Descriptor Systems," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, December.
    7. Hong Shi & Guangming Xie & Wenguang Luo, 2013. "Controllability of Linear Discrete‐Time Systems with Both Delayed States and Delayed Inputs," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    8. X. J. Wan & Y. P. Zhang & J. T. Sun, 2013. "Controllability of Impulsive Neutral Functional Differential Inclusions in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, March.
    9. Jinhua Wang & Hongjun Xiang, 2010. "Upper and Lower Solutions Method for a Class of Singular Fractional Boundary Value Problems with p -Laplacian Operator," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-12, September.
    10. Hong Shi & Guangming Xie & Wenguang Luo, 2012. "Controllability Analysis of Linear Discrete Time Systems with Time Delay in State," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-11, October.
    11. Shinn-Horng Chen & Wen-Hsien Ho & Jyh-Horng Chou, 2012. "Robust Local Regularity and Controllability of Uncertain TS Fuzzy Descriptor Systems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    12. Rabha W. Ibrahim, 2012. "Complex Transforms for Systems of Fractional Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, November.
    13. Hong Shi & Guangming Xie & Wenguang Luo, 2012. "Controllability Analysis of Linear Discrete Time Systems with Time Delay in State," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    14. Lianwen Wang, 2011. "Approximate Boundary Controllability for Semilinear Delay Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-10, August.
    15. Hong Shi & Guangming Xie & Wenguang Luo, 2013. "Controllability of Linear Discrete-Time Systems with Both Delayed States and Delayed Inputs," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-5, March.
    16. Hong Shi & Guangming Xie, 2012. "Controllability and Observability Criteria for Linear Piecewise Constant Impulsive Systems," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-24, September.
    17. Amar Debbouche & Dumitru Baleanu, 2012. "Exact Null Controllability for Fractional Nonlocal Integrodifferential Equations via Implicit Evolution System," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    18. N. I. Mahmudov, 2013. "Approximate Controllability of Fractional Sobolev-Type Evolution Equations in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, March.
    19. Amar Debbouche & Dumitru Baleanu, 2012. "Exact Null Controllability for Fractional Nonlocal Integrodifferential Equations via Implicit Evolution System," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, September.
    20. 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).
    21. X. J. Wan & Y. P. Zhang & J. T. Sun, 2013. "Controllability of Impulsive Neutral Functional Differential Inclusions in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    22. Lianwen Wang, 2011. "Approximate Boundary Controllability for Semilinear Delay Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
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    Cited by:

    1. Tao Zou & Jianfeng Qu & Yi Chai & Maoyun Guo & Congcong Liu, 2014. "Uniform Stability of a Class of Fractional‐Order Nonautonomous Systems with Multiple Time Delays," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    2. 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).
    3. Nien-Tsu Hu & Ter-Feng Wu & Sendren Sheng-Dun Xu & Hsu-Chih Huang, 2013. "Novel Observer‐Based Suboptimal Digital Tracker for a Class of Time‐Delay Singular Systems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    4. 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).

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