Skip to main content
SpringerLink
Log in

Representations of Linear Dynamic Systems

  • Chapter
  • First Online:
Decoupling Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 285))

Abstract

In this chapter, we will review some preliminary notions and results on linear systems that will be needed subsequently for the solution of various decoupling problems in later chapters. Multivariable linear dynamic systems and their representations are introduced. Polynomial and rational function matrices are studied in details. Matrix fraction descriptions and multivariable poles and zeros are covered. State-space realizations from matrix fraction descriptions are discussed. Model reduction is important in many ways, existing methods are highlighted and two algorithms taking care of stability of reduced models are presented. Conversions between continuous time and discrete time systems are reviewed and a technique with high accuracy and stability preservation is described.

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 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

2.6 Notes and References

  • Baratchart, L., M. Cardelli and M. Olivi (1991). Identification and rational L 2 approximation: a gradient algorithm. Automatica 27(2), pp.413–417.

    Article  MATH  MathSciNet  Google Scholar 

  • Callier, F.M. and C.A. Desoer (1982). Multivariable feedback systems.

    Google Scholar 

  • Chen, C.-T. (1984). Linear System Theory and Design. Holt, Rinehart and Winston. New York.

    Google Scholar 

  • Chen, T. and B. A. Francis (1991). H 2-optimal sampled-data control. IEEE Trans. Automatic Control 36(4), 387–397.

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  • Enns, D. (1984). Model reduction for control system design. Stanford University. Stanford, CA.

    Google Scholar 

  • Franklin, G. F., J. D. Powell and M. L. Workman (1990). Digital Control of Dynamic Systems. Addison-Wesley. Reading, Mass.

    MATH  Google Scholar 

  • Glover, K. (1984). All optimal Hankel norm approximations of linear multivariable systems and their l ∞ error bounds. IJC 39, 1115–1193.

    MATH  MathSciNet  Google Scholar 

  • Hyland, D. C. and D. S. Bernstein (1985). The optimal projection equations for model reduction and the relationships among the methods of Wilson, Skelton and Moore. IEEE Trans. Automatic Control AC-30, pp.1201–1211.

    Article  MathSciNet  Google Scholar 

  • Kailath, T. (1980). Linear systems. Prentice Hall.

    Google Scholar 

  • Keller, J. P. and B. D. O. Anderson (1992). A new approach to the discretization of continuous-time controllers. IEEE Trans. Automatic Control 37, 214–223.

    Article  MATH  MathSciNet  Google Scholar 

  • Kucera, V (1979). Discrete Linear Control. Academia. Prague.

    MATH  Google Scholar 

  • Kuo, B. C. (1980). Digital control systems. Holt, Rinehart and Winston. NY.

    Google Scholar 

  • Meier, L. and D. G. Luenberger (1967). Approximation of linear constant systems. IEEE Trans. Automatic Control AC-12, pp.585–588.

    Article  Google Scholar 

  • Moore, B. C. (1981). Principal component analysis in linear systems. IEEE Trans. Automatic Control AC-26, pp.17–32.

    Article  Google Scholar 

  • Pernebo, L. and L. M. Silverman (1982). Model reduction via balanced state space representation. IEEE Trans. Automatic Control AC-27(2), pp.382–387.

    Article  MathSciNet  Google Scholar 

  • Rafee, N., T. Chen and O. Malik (1997). A technique for optimal digital redesign of analog controllers. IEEE Transactions on Control System Technology 5(1), 89–99.

    Article  Google Scholar 

  • Rattan, K. S. (1984). Digitalization of existing continuous control system. IEEE Trans. Automatic Control AC-29(3), 282–285.

    Article  Google Scholar 

  • Rosenbrock, H. H. (1974). Computer-aided Control System Design. Academic Press. NY.

    Google Scholar 

  • Shieh, L. S., J. L. Zhang and J. W. Sunkel (1992). A new approach to the digital redesign of continuous-time controllers. Control Theory and Advanced Technology 8, 37–57.

    MathSciNet  Google Scholar 

  • Spanos, J. T., M. H. Milman and D. L. Mingori (1992). A new algorithm for L∞ optimal model reduction. Automatica 28(5), pp.897–909.

    Article  MATH  MathSciNet  Google Scholar 

  • Wang, Q. G. and X.P. Yang (2001). High performance conversions between continuous and discrete systems. signal processing.

    Google Scholar 

  • Wolovich, W. A. (1978). Skew prime polynomial matrices. IEEE Trans. Aut. Control AC-23, 880–887.

    Article  MathSciNet  Google Scholar 

  • Yang, Xueping (2001). Advanced Control Tuning for Time Delay Systems. PhD Thesis, National University of Singapore. Singapore.

    Google Scholar 

  • Zhou, K. (1995). Frequency-weighted L∞ norm and optimal Hankel norm model reduction. IEEE Trans. Automatic Control 40(10), pp.1687–1699.

    Article  MATH  Google Scholar 

Download references

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

(2003). Representations of Linear Dynamic Systems. In: Decoupling Control. Lecture Notes in Control and Information Sciences, vol 285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46151-5_2

Download citation

  • DOI: https://doi.org/10.1007/3-540-46151-5_2

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44128-1

  • Online ISBN: 978-3-540-46151-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation