Skip to main content
SpringerLink
Log in

On the Stability of a Switched Affine System for a Class of Switching Signals

  • CONTROL THEORY
  • Published:
Differential Equations Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

We study the problem of stability of the zero equilibrium of a switched affine system closed by a linear static state feedback. The concept of feasible control for a given set of switching signals is introduced, and a constructive condition for checking this property for an arbitrary linear feedback is obtained. A sufficient condition for the stability of the zero equilibrium of a switched affine system closed by a feasible control is formulated.

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

REFERENCES

  1. Rewienski, M. and White, J., Model order reduction for nonlinear dynamical systems based on trajectory piecewise-linear approximations, Linear Algebra Appl., 2006, vol. 415, pp. 426–454.

    Article  MathSciNet  MATH  Google Scholar 

  2. Johansson, M., Piecewise Linear Control System, Berlin–Heidelberg: Springer-Verlag, 2003.

    Book  Google Scholar 

  3. Rodrigues, L. and How, J., Synthesis of piecewise-affine controllers for stabilization of nonlinear systems, Proc. IEEE Conf. Decis. Control, 2004, vol. 3, pp. 2071–2076.

    Google Scholar 

  4. Filippov, A.F., Differentsial’nye uravneniya s razryvnoi pravoi chast’yu (Differential Equations with Discontinuous Right-Hand Side), Moscow: Nauka, 1985.

    MATH  Google Scholar 

  5. Li, C., Chen, G., and Liao, X., Stability of piecewise affine systems with application to chaos stabilization, Chaos, 2007, vol. 17, p. 023123.

    Article  MathSciNet  MATH  Google Scholar 

  6. Liberzon, D., Switching in Systems and Control, Boston: Springer Sci. + Bus. Media, 2003.

    Book  MATH  Google Scholar 

  7. Chernikov, S.N., Lineinye neravenstva (Linear Inequalities), Moscow: Nauka, 1968.

    Google Scholar 

  8. Demidovich, B.P., Lektsii po matematicheskoi teorii ustoichivosti (Lectures on the Mathematical Theory of Stability), Moscow: Nauka, 1967.

    Google Scholar 

  9. Fraysseix, H., Mendez, P., and Rosenstiehl, P., Bipolar orientations revisited, Discrete Appl. Math., 1995, vol. 56, pp. 426–454.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Funding

This work was supported by the Russian Science Foundation, project no. 22-21-00162.

Author information

Authors and Affiliations

  1. Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, Zhejiang, 310005, China

    A. S. Fursov

  2. Lomonosov Moscow State University, Moscow, 119991, Russia

    A. S. Fursov & P. A. Krylov

  3. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, 127051, Russia

    A. S. Fursov

Authors
  1. A. S. Fursov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. A. Krylov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to A. S. Fursov or P. A. Krylov.

Additional information

Translated by V. Potapchouck

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fursov, A.S., Krylov, P.A. On the Stability of a Switched Affine System for a Class of Switching Signals. Diff Equat 59, 563–571 (2023). https://doi.org/10.1134/S0012266123040110

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266123040110

Search

Navigation