Home Perfect nonlinear observers of fractional descriptor continuous-time nonlinear systems
Article
Licensed
Unlicensed Requires Authentication

Perfect nonlinear observers of fractional descriptor continuous-time nonlinear systems

  • Tadeusz Kaczorek EMAIL logo
Published/Copyright: June 23, 2016
Become an author with De Gruyter Brill
Author Information Explore this Subject
Fractional Calculus and Applied Analysis
From the journal Fractional Calculus and Applied Analysis Volume 19 Issue 3

Abstract

Perfect nonlinear fractional descriptor observers for fractional descriptor continuous-time nonlinear systems are proposed. Necessary and sufficient conditions for the existence of the observers are established. The design procedure of the nonlinear fractional observers is given. It is based on the elementary row (column) operations and reducing the singular matrix of the system to upper (lower) triangular form. The effectiveness of the procedure is demonstrated on a numerical example.

Key Words and Phrases: fractional descriptor nonlinear systems; design; perfect; descriptor; fractional; observer
MSC 2010: Primary 34K37; Secondary: 93C10, 93C35, 93C41

Acknowledgements

This work was supported by National Science Centre in Poland under Work2014/13/B/ST7/03467.

References

[1] Cuihong W. New delay-dependent stability criteria for descriptor systems with interval time delay Asian Journal of Control 14 No 1 2012 197 206 DOI: 10.1002/asjc.287Search in Google Scholar

[2] Dai L. Singular Control Systems, Lecture Notes in Control and Information Sciences Springer-Verlag Berlin 1989 DOI: 10.1007/BFb0002475Search in Google Scholar

[3] Dodig M. Stosic M. Singular systems, state feedbacks problem Linear Algebra and its Applications 431 No 8 2009 1267 1292 DOI: 10.1016/j.laa.2009.04.024Search in Google Scholar

[4] Duan G. Analysis and Design of Descriptor Linear Systems Springer-Verlag New York 2010 DOI: 10.1007/978-1-4419-6397-0Search in Google Scholar

[5] Fahmy M.M. O’Reilly J. Matrix pencil of closed-loop descriptor systems: infinite-eigenvalue assignment Int. J. Control 49 No 4 1989 1421 1431 DOI: 10.1080/00207178908559713Search in Google Scholar

[6] Gantmacher F.R. The Theory of Matrices Chelsea Publishing Co. New York 196010.1063/1.3062774Search in Google Scholar

[7] Kaczorek T. Checking of the positivity of descriptor linear systems with singular pencils Archives of Control Sciences 22 No 1 2012 77 86 DOI: 10.2478/v10170-011-0013-3Search in Google Scholar

[8] Kaczorek T. Descriptor fractional linear systems with regular pencils Asian Journal of Control 15 No 4 2013 1051 1064; DOI: 10.1002/asjc.579Search in Google Scholar

[9] Kaczorek T. Fractional descriptor observers for fractional descriptor continuous-time linear system Archives of Control Sciences 24 No 1 2014 39 5 2 DOI: 10.2478/acsc-2014-0003Search in Google Scholar

[10] Kaczorek T. Fractional positive continuous-time linear systems and their reachability Int. J. Appl. Math. Comput. Sci. 18 No 2 2008233-228; DOI: 10.2478/v10006-008-0020-0Search in Google Scholar

[11] Kaczorek T. Full-order perfect observers for continuous-time linear systems Bull. Pol. Acad. Sci.: Tech. 49 No 4 2001 549 558Search in Google Scholar

[12] Kaczorek T. Infinite eigenvalue assignment by an output feedback for singular systems Int. J. Appl. Math. Comput. Sci. 14 No 1 2004 19 23 DOI: 10.3182/20050703-6-CZ-1902.00564Search in Google Scholar

[13] Kaczorek T. Linear Control Systems: Analysis of Multivariable Systems J. Wiley & Sons New York 1992Search in Google Scholar

[14] Kaczorek T. Perfect observers of fractional descriptor continuous-time linear system In: Advances in Modelling and Control of Non-integer Order Systems 320 2015 3 12 Springer DOI: 10.1007/978-3-319-09900-2_1Search in Google Scholar

[15] Kaczorek T. Positive fractional continuous-time linear systems with singular pencils Bull. Pol. Ac.: Tech. 60 No 1 2012 9 12 DOI: 10.2478/v10175-012-0002-0Search in Google Scholar

[16] Kaczorek T. Positive linear systems consisting of n subsystems with different fractional orders IEEE Trans. on Circuits and Systems 58 No 6 2011 1203 1210 DOI: 10.1109/TCSI.2010.2096111Search in Google Scholar

[17] Kaczorek T. Reduced-order fractional descriptor observers for fractional descriptor continuous-time linear system Bull. Pol. Acad. Sci.: Tech. 62 No 4 2014 889 895 DOI: 10.2478/bpasts-2014-0098Search in Google Scholar

[18] Kaczorek T. Selected Problems of Fractional Systems Theory Springer-Verlag Berlin 2011 DOI: 10.1007/978-3-642-20502-6Search in Google Scholar

[19] Kociszewski R. Observer synthesis for linear discrete-time systems with different fractional orders Measurements Automation Robotics (PAR) 17 No 2 2013 376 381(in Polish, CD-ROM)Search in Google Scholar

[20] Kucera V. Zagalak P. Fundamental theorem of state feedback for singular systems Automatica 24 No 5 1988 653 658 DOI: 10.1016/0005-1098(88)901124Search in Google Scholar

[21] Lewis F.L. Descriptor systems: Expanded descriptor equation and Markov parameters IEEE Trans. Autom. Contr. 28 No 5 1983 623 627 DOI: 10.1109/TAC.1983.1103285Search in Google Scholar

[22] Luenberger D.G. Dynamic equations in descriptor form IEEE Trans. Autom. Contr. 22 No 3 1977 312 321 DOI: 10.1109/TAC.1977.1101502Search in Google Scholar

[23] Luenberger D.G. Time-invariant descriptor systems Automatica 14 No 5 1978 473 480 DOI: 10.1016/0005-1098(78)900067Search in Google Scholar

[24] N’Doye I. Darouach M. Voos H. Zasadzinski M. Design of unknown input fractional-order observers for fractional-order systems Int. J. Appl. Math. Comput. Sci. 23 No 3 2013 491 500 DOI: 10.2478/amcs-2013-0037Search in Google Scholar

[25] Podlubny I. Fractional Differential Equations Academic Press New York 1999Search in Google Scholar

[26] Van Dooren P. The computation of Kronecker's canonical form of a singular pencil Linear Algebra and its Applications 24 1979 103 140 DOI: 10.1016/0024-3795(79)90035-1Search in Google Scholar

[27] Virnik E. Stability analysis of positive descriptor systems Linear Algebra and its Applications 429 No 10 2008 2640 2659 DOI: 10.1016/j.laa.2008.03.002Search in Google Scholar

Received: 2015-6-1
Revised: 2016-2-7
Published Online: 2016-6-23
Published in Print: 2016-6-1

© 2016 Diogenes Co., Sofia

Articles in the same Issue

  1. Frontmatter
  2. Editorial Note
  3. FCAA related news, events and books (FCAA-volume 19-3-2016)
  4. Survey Paper
  5. Fractional integrals and derivatives: mapping properties
  6. Research Paper
  7. Riesz fractional integrals in grand lebesgue spaces on ℝn
  8. Survey Paper
  9. United lattice fractional integro-differentiation
  10. Research Paper
  11. Integral equations of fractional order in Lebesgue spaces
  12. Research Paper
  13. General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems
  14. Research Paper
  15. Multilinear integral operators in weighted grand Lebesgue spaces
  16. Research Paper
  17. Fractional integration operator on some radial rays and intertwining for the Dunkl operator
  18. Research Paper
  19. Pseudo almost automorphy of semilinear fractional differential equations in Banach Spaces
  20. Research Paper
  21. Existence and uniqueness of global solutions of caputo-type fractional differential equations
  22. Research Paper
  23. Perfect nonlinear observers of fractional descriptor continuous-time nonlinear systems
https://doi.org/10.1515/fca-2016-0041
Keywords for this article
fractional descriptor nonlinear systems; design; perfect; descriptor; fractional; observer

Articles in the same Issue

  1. Frontmatter
  2. Editorial Note
  3. FCAA related news, events and books (FCAA-volume 19-3-2016)
  4. Survey Paper
  5. Fractional integrals and derivatives: mapping properties
  6. Research Paper
  7. Riesz fractional integrals in grand lebesgue spaces on ℝn
  8. Survey Paper
  9. United lattice fractional integro-differentiation
  10. Research Paper
  11. Integral equations of fractional order in Lebesgue spaces
  12. Research Paper
  13. General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems
  14. Research Paper
  15. Multilinear integral operators in weighted grand Lebesgue spaces
  16. Research Paper
  17. Fractional integration operator on some radial rays and intertwining for the Dunkl operator
  18. Research Paper
  19. Pseudo almost automorphy of semilinear fractional differential equations in Banach Spaces
  20. Research Paper
  21. Existence and uniqueness of global solutions of caputo-type fractional differential equations
  22. Research Paper
  23. Perfect nonlinear observers of fractional descriptor continuous-time nonlinear systems
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 16.11.2025 from https://www.degruyterbrill.com/document/doi/10.1515/fca-2016-0041/html
Scroll to top button