Skip to main content
SpringerLink
Log in

Nonfragile Controller Design for Linear Markovian Jumping Parameters Systems

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

This paper deals with the uncertain class of continuous-time linear systems with Markovian jumping parameters. A design method for a nonfragile robust controller for this class of systems is proposed when the uncertainties in the system matrices are of the norm-bounded type. An LMI based sufficient condition is developed. The methodology used is based mainly on the Lyapunov approach. A numerical example is presented to show the usefulness of the proposed results.

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. Krasovskii, N.N., and Lidskii, E.A., Analysis Design of Controllers in Systems with Random Attributes, Part 1, Automation and Remote Control, Vol.35, pp.1021-1025, 1961.

    Google Scholar 

  2. Boukas, E.K., and Liu, Z.K., Deterministic and Stochastic Systems with Time Delay, Birkhauser, Boston, Massachusetts, 2002.

    Google Scholar 

  3. Mao, X., Stability of Stochastic Differential Equations with Markovian Switching, Stochastic Processes and Their Applications, Vol.79, pp.45-67, 1999.

    Google Scholar 

  4. Shi, P., and Boukas, E.K., H ∞ Control for Markovian Jumping Linear Systems with Parametric Uncertainty, Journal of Optimization Theory and Applications, Vol.95, pp.75-99, 1997.

    Google Scholar 

  5. Shi, P., Boukas, E.K., and Agarwal, R.K., Control of Markovian Jump Discrete-Time Systems with Norm-Bounded Uncertainty and Unknown Delay, IEEE Transactions on Automatic Control, Vol. 44, pp. 2139-2144, 1999.

    Google Scholar 

  6. Wang, Z., Qiao, H., and Burnham, K.J., On the Stabilization of Bilinear Uncertain Time-Delay Stochastic Systems with Markovian Jumping Parameters, IEEE Transactions on Automatic Control, Vol. 47, pp. 460-646, 2002.

    Google Scholar 

  7. Keel, L.H., and Bhattacharyya, Robust, Fragile, or Optimal, IEEE Transactions on Automatic Control, Vol. 42, pp.1098-1105, 1997.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. GERAD and Mechanical Engineering Department, École Polytechnique de Montréal, Montréal, Québec, Canada

    E. K. Boukas (Professor)

Authors
  1. E. K. Boukas
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Boukas, E.K. Nonfragile Controller Design for Linear Markovian Jumping Parameters Systems. Journal of Optimization Theory and Applications 122, 241–255 (2004). https://doi.org/10.1023/B:JOTA.0000042520.85247.0c

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:JOTA.0000042520.85247.0c

Search

Navigation