Skip to main content

Linear \(\mathcal{H}_{\infty }\) Control of Time-Varying Systems

  • Chapter
  • First Online:
Advanced H∞ Control

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

  • 1490 Accesses

Abstract

This chapter presents the generalization of the \(\mathcal{H}_{\infty }\) synthesis to linear time-varying systems and to linear periodic systems, in particular.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
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

References

  1. Brogliato, B., Lozano, R., Maschke, B., Egeland, O.: Dissipative Systems Analysis and Control—Theory and Applications, 2nd edn. Springer, London (2007)

    Book  MATH  Google Scholar 

  2. Chung, C., Hauser, J.: Nonlinear \(\mathcal{H}_{\infty }\)-control around periodic orbits. Syst. Control Lett. 30, 127–137 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  3. Colaneri, P.: Continuous-time periodic systems in \(\mathcal{H}_{2}\) and \(\mathcal{H}_{\infty }\)—part 1: theoretical aspects. Kybernetika 36(2), 211–242 (2000)

    MATH  MathSciNet  Google Scholar 

  4. Colaneri, P.: Continuous-time periodic systems in \(\mathcal{H}_{2}\) and \(\mathcal{H}_{\infty }\)—part 2: state feedback problems. Kybernetika 36(3), 329–350 (2000)

    MATH  MathSciNet  Google Scholar 

  5. Liusternik, L., Sobolev, V.: Elements of Functional Analysis. Frederick Ungar Publishing Company, New York (1961)

    Google Scholar 

  6. Orlov, Y., Acho, L., Solis, V.: Nonlinear \(\mathcal{H}_{\infty }\)-control of time varying systems. In: Proceedings of 38th Conference on Decision and Control, Phoenix, pp. 3764–3769 (1999)

    Google Scholar 

  7. Ravi, R., Nagpal, K., Khargonekar, P.: \(\mathcal{H}_{\infty }\) control of linear time-varying systems: a state-space approach. SIAM J. Control Optim. 29, 1394–1413 (1991)

    Google Scholar 

  8. Shayman, M.: Inertia theorems for the periodic Liapunov equation and periodic Riccati equations. Syst. Control Lett. 4, 27–32 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  9. Vidyasagar, M.: Nonlinear Systems Analysis. Prentice Hall, Englewood Cliffs (1978)

    Google Scholar 

  10. Xie, L., de Souza, C.: State estimation for linear periodic systems. In: Proceedings of the 24th IEEE Conference on Decision and Control, San Diego, pp. 3188–3193 (1990)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media, New York

About this chapter

Cite this chapter

Orlov, Y.V., Aguilar, L.T. (2014). Linear \(\mathcal{H}_{\infty }\) Control of Time-Varying Systems. In: Advanced H∞ Control. Systems & Control: Foundations & Applications. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4939-0292-7_3

Download citation

Publish with us

Policies and ethics