Rejection of persistent, bounded disturbances for sampled-data systems

  • Bassam Bamieh
  • Munther A. Dahleh
  • J. Boyd Pearson
Conference paper
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 183)


In this paper, a complete solution for the 1 sampled-data problem is furnished for arbitrary plants. Then 1 sampled-data problem is described as follows: Given a continuous-time plant, with continuous-time performance objectives, design a digital controller that delivers this performance. This problem differs from the s-tandard discrete-time methods in that it takes into consideration the inter-sampling behaviour of the closed loop system. The resulting closed loop system dynamics consists of both continuous-time and discrete-time dynamics and thus such systems are known as “Hybrid” systems. It is shown that given any degree of accuracy, there exists a standard discrete-time 1 problem, which can be determined apriori, such that for any controller that achieves a level of performance for the discrete-time problem, the same controller achieves the same performance within the prescribed level of accuracy if implemented as a sampled-data controller.


Close Loop System Digital Controller Continuous Time Signal Linear Periodic System Linear Continuous Time System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    B. Bamieh, M.A. Dahleh and J.B. Pearson, ‘Minimization of the L induced norm for sampled-data systems,’ Rice University Technical Report, Houston, TX, June 1991.Google Scholar
  2. [2]
    B. Bamieh and J.B. Pearson, ‘A General Framework for Linear Periodic Systems with Application to H Sampled-Data Control', to appear in IEEE Trans. on Aut. Control. Google Scholar
  3. [3]
    B. Bamieh, J.B. Pearson, B.A. Francis, A. Tannenbaum, ‘A Lifting Technique for Linear Periodic Systems with Applications to Sampled-Data Control', to appear in Systems and Controls Letters. Google Scholar
  4. [4]
    T. Chen and B. Francis, ‘On the L 2 induced 26 26 norm of a sampled-data system', Systems and Control Letters 1990, v.15, 211–219.zbMATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    M.A. Dahleh and J.B. Pearson, ‘ 1-optimal feedback control for MIMO discrete-time systems', in Trans. Aut. Control, AC-32, 1987.Google Scholar
  6. [6]
    C.A. Desoer and M. Vidyasagar, Feedback Systems: Input-Output Properties, Academic Press, New York, 1975.zbMATHGoogle Scholar
  7. [7]
    G. Dullerud and B. Francis, ‘L 1 Performance in Sampled-Data Systems', preprint, Submitted to IEEE Trans. on Aut. Control. Google Scholar
  8. [8]
    B.A. Francis and T.T. Georgiou, ‘Stability theory for linear time-invariant plants with periodic digital controllers', IEEE Trans. Aut. Control, AC-33, pp. 820–832, 1988.CrossRefMathSciNetGoogle Scholar
  9. [9]
    P.T. Kabamba and S. Hara, ‘Worst case analysis and design of sampled data control systems', Preprint.Google Scholar
  10. [10]
    J.S. McDonald and J.B. Pearson, ‘ 1-Optimal Control of Multivariable Systems with Output Norm Constraints', Automatica, vol. 27, no. 3, 1991.Google Scholar
  11. [11]
    N. Sivashankar and Pramod P. Khargonekar, ‘L -Induced Norm of Sampled-Data Systems', Proc. of the CDC, 1991.Google Scholar
  12. [12]
    P.M. Thompson, G. Stein and M. Athans, ‘Conic sectors for sampled-data feedback systems,’ System and Control Letters, Vol 3, pp. 77–82, 1983.zbMATHCrossRefGoogle Scholar
  13. [13]
    H.T. Toivonen, 'sampled-data control of continuous-time systems with an H optimality criterion', Chemical Engineering, Abo Akademi, Finland, Report 90-1, January 1990.Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Bassam Bamieh
    • 1
  • Munther A. Dahleh
    • 2
  • J. Boyd Pearson
    • 1
  1. 1.Dept. of Electrical and Computer EngineeringRice UniversityHouston
  2. 2.Laboratory of Information and Decision SystemsMassachusetts Institute of TechnologyCambridge

Personalised recommendations