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Finite-time L 2−L ∞ filtering for nonlinear stochastic systems based on a novel stochastic finite-time stability theorem

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  • Control Theory and Applications
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Abstract

This paper presents a novel stochastic finite-time stability theorem and gives its application in the finite-time L 2−L ∞ filter design for nonlinear stochastic systems. Different form the frequently-used stochastic finite-time stability result, the proposed one does not require that all the states have the same fractional order exponent. Based on this result, a sufficient condition is given for nonlinear stochastic systems to possess the finite-time L 2−L ∞ performance with a prescribed gain. Further, an existence condition of the finite-time L 2−L ∞ filter with a prescribed disturbance attenuation level is given for nonlinear stochastic systems with external disturbance inputs. The effectiveness of the obtained results is illustrated by an example.

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Author information

Authors and Affiliations

  1. Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin, 150001, China

    Mingzhe Hou & Gunagren Duan

  2. Harbin Institute of Technology Shenzhen Graduate School, Shenzhen, 518055, China

    Aiguo Wu

Authors
  1. Mingzhe Hou
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  2. Aiguo Wu
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  3. Gunagren Duan
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Corresponding author

Correspondence to Mingzhe Hou.

Additional information

Recommended by Associate Editor Choon Ki Ahn under the direction of Editor PooGyeon Park. This work was supported by the Major Program of National Natural Science Foundation of China under Grant Numbers 61690210 and 61690212, National Natural Science Foundation of China (No.61203125, 61503100), China Postdoctoral Science Foundation (No. 2014M550189), Heilongjiang Postdoctoral Fund (No. LBH-Z13076).

Mingzhe Hou received his BEng and PhD degrees in Control Science and Engineering from Harbin Institute of Technology in 2005 and 2011, respectively. He became an Lecturer in 2013 at Harbin Institute of Technology, China. His research interests include nonlinear filtering and control, aircraft guidance and control.

Aiguo Wu received his BEng degree in Automation in July 2002, MEng degree in Navigation, Guidance and Control in July 2004 and PhD degree in Control Science and Engineering in Nov. 2008 all from Harbin Institute of Technology. In Oct. 2008, he joined Harbin Institute of Technology Shenzhen Graduate School, where he is now a Professor. He visited City University of Hong Kong from March 2009 to March 2011 as a Research Fellow. He is a Reviewer for American Mathematical Review. He was an Outstanding Reviewer for IEEE Transactions on Automatic Control. He received the National Excellent Doctoral Dissertation Award in 2011 from the Academic Degrees Committee of the State Council and the Ministry of Education of P. R. China. He was supported by the Program for New Century Excellent Talents in University in 2011. His research interests include descriptor systems, conjugate product of polynomials, and robust control.

Guang-Ren Duan received his B.Sc. degree in Applied Mathematics, and both his M.Sc. and Ph.D. degrees in Control Systems Theory. From 1989 to 1991, he was a post-doctoral researcher at Harbin Institute of Technology, where he became a professor of control systems theory in 1991. Prof. Duan visited the University of Hull, UK, and the University of Sheffield, UK from December 1996 to October 1998, and worked at the Queen’s University of Belfast, UK from October 1998 to October 2002. Since August 2000, he has been elected Specially Employed Professor at Harbin Institute of Technology sponsored by the Cheung Kong Scholars Program of the Chinese government. He is currently the Director of the Center for Control Systems and Guidance Technology at Harbin Institute of Technology. His main research interests include robust control, eigenstructure assignment, descriptor systems, missile autopilot control and magnetic bearing control. Dr. Duan is a Charted Engineer in the UK, a Senior Member of IEEE and a Fellow of IEE.

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Hou, M., Wu, A. & Duan, G. Finite-time L 2−L ∞ filtering for nonlinear stochastic systems based on a novel stochastic finite-time stability theorem. Int. J. Control Autom. Syst. 15, 489–497 (2017). https://doi.org/10.1007/s12555-015-0385-4

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  • DOI: https://doi.org/10.1007/s12555-015-0385-4

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