Skip to main content
SpringerLink
Log in
Book cover

Encyclopedia of Systems and Control pp 1–11Cite as

Optimal Sampled-Data Control

  • 385 Accesses

Abstract

This article gives a brief overview on the modern development of sampled-data control. Sampled-data systems intrinsically involve a mixture of two different time sets, one continuous and the other discrete. Due to this, sampled-data systems cannot be characterized in terms of the standard notions of transfer functions, steady-state response, or frequency response. The technique of lifting resolves this difficulty and enables the recovery of such concepts and simplified solutions to sampled-data H ∞ and H 2 optimization problems. We review the lifting point of view, its application to such optimization problems, and finally present an instructive numerical example.

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

Bibliography

  • Åström KJ, Wittenmark B (1996) Computer controlled systems—theory and design, 3rd edn. Prentice Hall, Upper Saddle River

    Google Scholar 

  • Bamieh B, Pearson JB (1992) A general framework for linear periodic systems with applications to H ∞ sampled-data control. IEEE Trans Autom Control 37:418–435

    Article  MATH  MathSciNet  Google Scholar 

  • Bamieh B, Pearson JB, Francis BA, Tannenbaum A (1991) A lifting technique for linear periodic systems with applications to sampled-data control systems. Syst Control Lett 17:79–88

    Article  MATH  MathSciNet  Google Scholar 

  • Cantoni M, Glover K (1997) H ∞ sampled-data synthesis and related numerical issues. Automatica 33:2233–2241

    Article  MATH  MathSciNet  Google Scholar 

  • Chen T, Francis BA (1990) On the \(\mathcal{L}_{2}\)-induced norm of a sampled-data system. Syst Control Lett 15:211–219

    Article  MATH  MathSciNet  Google Scholar 

  • Chen T, Francis BA (1995) Optimal sampled-data control systems. Springer, New York

    Book  MATH  Google Scholar 

  • Jury EI (1958) Sampled-data control systems. Wiley, New York

    MATH  Google Scholar 

  • Kabamba PT, Hara S (1993) Worst case analysis and design of sampled data control systems. IEEE Trans Autom Control 38:1337–1357

    Article  MATH  MathSciNet  Google Scholar 

  • Nagahara M, Yamamoto, Y (2012) Frequency domain min-max optimization of noise-shaping Delta-Sigma modulators. IEEE Trans Signal Process 60:2828–2839

    Article  MathSciNet  Google Scholar 

  • Ragazzini JR, Franklin GF (1958) Sampled-data control systems. McGraw-Hill, New York

    MATH  Google Scholar 

  • Sivashankar N, Khargonekar PP (1994) Characterization and computation of the \(\mathcal{L}_{2}\)-induced norm of sampled-data systems. SIAM J Control Optim 32:1128–1150

    Article  MATH  MathSciNet  Google Scholar 

  • Tadmor G (1991) Optimal \(\mathcal{H}_{\infty }\) sampled-data control in continuous time systems. In: Proceedings of ACC’91, Boston, Massachusetts, pp 1658–1663

    Google Scholar 

  • Toivonen HT (1992) Sampled-data control of continuous-time systems with an \(\mathcal{H}_{\infty }\) optimality criterion. Automatica 28:45–54

    Article  MATH  MathSciNet  Google Scholar 

  • Yamamoto Y (1990) New approach to sampled-data systems: a function space method. In: Proceedings of 29th CDC, Honolulu, Hawaii, pp 1882–1887

    Google Scholar 

  • Yamamoto Y (1993) On the state space and frequency domain characterization of \({H}^{\infty }\)-norm of sampled-data systems. Syst Control Lett 21:163–172

    Article  MATH  Google Scholar 

  • Yamamoto Y (1994) A function space approach to sampled-data control systems and tracking problems. IEEE Trans Autom Control 39:703–712

    Article  MATH  Google Scholar 

  • Yamamoto Y (1999) Digital control. In: Webster JG (ed) Wiley encyclopedia of electrical and electronics engineering, vol 5. Wiley, New York, pp 445–457

    Google Scholar 

  • Yamamoto Y (2012) From vector spaces to function spaces—introduction to functional analysis with applications. SIAM, Philadelphia

    Book  MATH  Google Scholar 

  • Yamamoto Y, Khargonekar PP (1996) Frequency response of sampled-data systems. IEEE Trans Autom Control 41:166–176

    Article  MATH  MathSciNet  Google Scholar 

  • Yamamoto Y, Nagahara M, Khargonekar PP (2012) Signal reconstruction via \({H}^{\infty }\) sampled-data control theory—Beyond the Shannon paradigm. IEEE Trans Signal Process 60:613–625

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University, Sakyo-ku Yoshida-Honmachi, 606-8501, Kyoto, Japan

    Yutaka Yamamoto Ph.D, Professor

Authors
  1. Yutaka Yamamoto Ph.D, Professor
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yutaka Yamamoto Ph.D, Professor .

Editor information

Editors and Affiliations

  1. Electrical and Computer Engineering, Boston University, Boston, Massachusetts, USA

    John Baillieul

  2. Automation and Control Solutions, Honeywell, Golden Valley, Minnesota, USA

    Tariq Samad

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag London

About this entry

Cite this entry

Yamamoto, Y. (2013). Optimal Sampled-Data Control. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_205-1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_205-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, London

  • Online ISBN: 978-1-4471-5102-9

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

Publish with us

Policies and ethics

Chapter history

  1. Latest

    Optimal Sampled-Data Control
    Published:
    14 November 2019

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_205-2

  2. Original

    Optimal Sampled-Data Control
    Published:
    24 March 2014

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_205-1

Search

Navigation