Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (5): 1529-1544.

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On the Observer Design for Fractional Singular Linear Systems

Zaiyong Feng1,2(),Ning Chen3,*(),Yongpeng Tai4,Zhengrong Xiang2()   

  1. 1 Department of Basic Sciences, Nanjing Institute of Railway Technology, Nanjing 210031
    2 School of Automation, Nanjing University of Science and Technology, Nanjing 210094
    3 College of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing 210037
    4 College of Automobile and Traffic Engineering, Nanjing Forestry University, Nanjing 210037
  • Received:2020-09-24 Online:2021-10-26 Published:2021-10-08
  • Contact: Ning Chen;
  • Supported by:
    the NSFC(61873128);the NSF of the Jiangsu Higher Education Institution of China(17KJB120008);the Jiangsu Rail Transit Control Engineering Technology Research and Development Center(KFJ2010);the Qing Lan Project of the Jiangsu Higher Education Institutions;Qing Lan Project of Nanjing Institute of Railway Technology


The paper discussed the Caputo fractional derivatives of impulse function $\delta(t) $, i.e., ${^C_0}{D}_t^\alpha\delta(t) $ and its Laplace transform, the distributional solution of Fractional Singular Linear Systems (FSLS) was consequently obtained. Based on the distributional solution of the system, the asymptotic stability theorem for FSLS was given, and the existence theorem of state observer for FSLS was proved. A simplified design method of full state observer for FSLS was investigated and summarized by pole assignment only for the slow subsystem. Finally, a state observer as an example was designed to verify the effectiveness of the proposed method.

Key words: Fractional singular linear system, Caputo fractional derivatives, Distributional solution, Asymptotic stability, State observer

CLC Number: 

  • TP13