Skip to main content
SpringerLink
Log in

Control with Sample-Data Measurements

  • Chapter
  • First Online:
Attractive Ellipsoids in Robust Control

Part of the book series: Systems & Control: Foundations & Applications ((SCFA))

Abstract

In this chapter, we formulate our main problem and discuss some necessary mathematical concepts related to feedback control design for nonlinear systems under sample-data output measurements. Then we present a theoretical analysis of an extended version of the invariant ellipsoid method. Then two feedbacks are analyzed:

  • a linear feedback proportional to the current state estimate obtained by a Luenberger-type estimator; and

  • a full-order linear dynamic controller governed by a linear ordinary differential equation with available sample data as input.

Then we construct a minimal attractive ellipsoid that guarantees stability of the system in a practical sense by varying all parameters of the suggested feedbacks. The associated numerical techniques are also presented. An implementable algorithm for the constructive treatment of the robust control design problem is proposed.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Bibliography

  • Basar, T., & Olsted, G. J. (1999). Dynamic noncooperative game theory. Philadelphia: SIAM.

    MATH  Google Scholar 

  • Duncan, G., & Schweppe, F. (1971). Control of linear dynamic systems with set constrained disturbances. IEEE Transactions on Automatic Control, 16, 411–423.

    Article  Google Scholar 

  • Fridman, E. (2006). Descriptor discretized Lyapunov functional method: analysis and design. IEEE Transactions on Automatic Control, 51, 890–897.

    Article  MathSciNet  Google Scholar 

  • Fridman, E. (2010). A refined input delay approach to sampled-data control. Automatica, 46, 421–427.

    Article  MathSciNet  MATH  Google Scholar 

  • Fridman, E., & Orlov, Y. (2007). On stability of linear parabolic distributed parameter systems with time-varying delays. In Proceedings of the 46th Conference on Decision and Control (pp. 1597–1602), New Orlean, USA.

    Google Scholar 

  • Fridman, E., & Shaked, U. (2002). An improved stabilization method for linear time-delay systems. IEEE Transaction on Automatic Control, 47(11), 1931–1937.

    Article  MathSciNet  Google Scholar 

  • Gu, K., Kharitonov, V., & Chen, J. (2003). Stability of time-delay systems. New York: Birkhäuser.

    Book  MATH  Google Scholar 

  • Kurzhanski, A., & Veliov, V. (1994). Modeling techniques and uncertain systems. New York: Birkhäuser.

    Google Scholar 

  • Leonhard, W. (1966). Control of electrical drives. Berlin: Springer.

    Google Scholar 

  • Michel, A., Hou, L., & Liu, D. (2007). Stability of dynamical systems. New York: Birkhäuser.

    Google Scholar 

  • Polyak, B. T., Nazin, S., Durieu, C., & Walter, E. (2004). Ellipsoidal parameter or state estimation under model uncertainty. Automatica, 40, 1171–1179. ellipsoids/polyak2004.pdf.

    Google Scholar 

  • Polyak, B. T., & Topunov, M. V. (2008) Suppression of bounded exogenous disturbances: Output feedback. Automation and Remote Control, 69, 801–818. ellipsoids/polyak2008.pdf.

    Google Scholar 

  • Polyakov, A., & Poznyak, A. (2009). Lyapunov function design for finite-time convergence analysis: “Twisting” controller for second-order sliding mode realization. Automatica, 45, 444–448.

    Article  MathSciNet  MATH  Google Scholar 

  • Poznyak, A. (2008). Advanced mathematical tools for automatic control engineers: Deterministic techniques. Amsterdam: Elsevier.

    Google Scholar 

  • Pytlak, R. (1999). Numerical methods for optimal control problems with state constraints. Berlin: Springer.

    MATH  Google Scholar 

  • Sontag, E. (1998). Mathematical control theory. New York: Springer.

    Book  MATH  Google Scholar 

  • Yakubovich, E. (1976). Solution of the optimal control problem for the linear discrete systems. Automation and Remote Control, 36, 1447–1453.

    MathSciNet  Google Scholar 

  • Zhou, K., Doyle, J., & Glover, K. (1996). Robust and optimal control. Upper Saddle River, NJ: Prentice Hall.

    Google Scholar 

  • Zubov, V. (1962). Mathematical methods for the study of automatic control systems. New York: Pergamon Press.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Automatic Control Department, Centro de Investigacion y Estudios Avanzados, México, Distrito Federal, Mexico

    Alexander Poznyak

  2. Non-A, INRIA-LNE, Villeneuve d’Ascq, Nord, France

    Andrey Polyakov

  3. Faculty of Electronic and Biomedical Engineering, University of Antonio Nariño, Neiva, HUILA, Colombia

    Vadim Azhmyakov

Authors
  1. Alexander Poznyak
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrey Polyakov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vadim Azhmyakov
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Poznyak, A., Polyakov, A., Azhmyakov, V. (2014). Control with Sample-Data Measurements. In: Attractive Ellipsoids in Robust Control. Systems & Control: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-09210-2_5

Download citation

Publish with us

Policies and ethics

Search

Navigation