Skip to main content
SpringerLink
Log in

Robust Controllability of Linear Differential-Algebraic Equations with Unstructured Uncertainty

  • Published:
Journal of Applied and Industrial Mathematics Aims and scope Submit manuscript

Abstract

We consider the linear stationary systems of ordinary differential equations (ODEs) that are unsolvedwith respect to the derivative of the unknown vector-function and degenerate identically in the domain of definition. These systems are usually called differential-algebraic equations (DAEs). The measure of how a system of DAEs is unsolved with respect to the derivative is an integer which is called the index of the system of DAEs. The analysis is carried out under the assumption of existence of a structural form with separated differential and algebraic subsystems. We investigate the robust controllability of these systems (controllability in the conditions of uncertainty). The sufficient conditions for the robust complete and R-controllability of a system of DAEs with the indices 1 and 2 are obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. C. Lin, J. L. Wang, and C.-B. Soh, “Necessary and Sufficient Conditions for the Controllability of Linear Interval Descriptor Systems,” Automatica 34 (3), 363–367 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  2. J. H. Chou, S. H. Chen, and R. F. Fung, “Sufficient Conditions for the Controllability of Linear Descriptor Systems with Both Time-Varying Structured and Unstructured Parameter Uncertainties,” IMA J. Math. Control Inform. 18 (4), 469–477 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  3. C. Lin, J. L. Wang, and C.-B. Soh, “Robust C-Controllability and/or C-Observability for Uncertain Descriptor Systemswith Interval Perturbation inAll Matrices,” IEEE Trans.Automat. Control 44 (9), 1768–1773 (1999).

    Article  MathSciNet  MATH  Google Scholar 

  4. C. Lin, J. L. Wang, C.-B. Soh, and G. H. Yang, “Robust Controllability and Robust Closed-Loop Stability with Static Output Feedback for a Class of Uncertain Descriptor Systems,” Linear Algebra Appl. 297 (1–3), 133–155 (1999).

    Article  MathSciNet  MATH  Google Scholar 

  5. J.-H. Chou, S.-H. Chen, and Q.-L. Zhang, “Robust Controllability for Linear Uncertain Descriptor Systems,” Linear Algebra Appl. 414 (2–3), 632–651 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  6. A. A. Shcheglova and P. S. Petrenko, “The R-Observability and R-Controllability of Linear Differential-Algebraic Systems,” Russian Mathematics 56 (3), 66–82 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  7. A. A. Shcheglova and P. S. Petrenko, “Stabilizability of Solutions to Linear and Nonlinear Differential-Algebraic Equations,” J.Math. Sci. 196 (4), 596–615 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  8. A. A. Shcheglova and P. S. Petrenko, “Stabilization of Solutions for Nonlinear Differential-Algebraic Equations,” Automation and Remote Control 76 (4), 573–588 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  9. P. S. Petrenko, “Local R-Observability of Differential-Algebraic Equations,” J. Siberian Federal Univ. Mathematics & Physics 9 (3), 353–363 (2016).

    Article  Google Scholar 

  10. P. S. Petrenko, “Differential Controllability of Linear Systems of Differential-Algebraic Equations,” J. Siberian Federal Univ. Mathematics & Physics 10 (3), 320–329 (2017).

    Article  MathSciNet  Google Scholar 

  11. F. R. Gantmakher, The Theory of Matrices (Nauka, Moscow, 1988) [in Russian].

    MATH  Google Scholar 

  12. A. A. Shcheglova, “Controllability of Nonlinear Algebraic Differential Systems,” Automation and Remote Control 69 (10), 1700–1722 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  13. V. A. Trenogin, Functional Analysis (Nauka, Moscow, 1980) [in Russian].

    MATH  Google Scholar 

  14. V. Mehrmann and T. Stykel, “Descriptor Systems: A General Mathematical Framework for Modelling, Simulation and Control,” Automatisierungstechnik 54 (8), 405–415 (2006).

    Google Scholar 

  15. A. A. Shcheglova, “The Solvability of the Initial Problem for a Degenerate Linear Hybrid System with Variable Coefficients,” Russian Mathematics 54 (9), 49–61 (2010).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Matrosov Institute of System Dynamics and Control Theory, ul. Lermontovа 134, Irkutsk, 664033, Russia

    P. S. Petrenko

Authors
  1. P. S. Petrenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. S. Petrenko.

Additional information

Original Russian Text © P.S. Petrenko, 2018, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2018, Vol. XXI, No. 3, pp. 104–115.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Petrenko, P.S. Robust Controllability of Linear Differential-Algebraic Equations with Unstructured Uncertainty. J. Appl. Ind. Math. 12, 519–530 (2018). https://doi.org/10.1134/S1990478918030122

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1990478918030122

Keywords

Search

Navigation