Time-varying vs. time-invariant compensation for rejection of persistent bounded disturbances and robust stabilization

J. S. Shamma*, M. A. Dahleh

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Summary form only given, as follows. Consideration was given to time-varying compensation for linear time-invariant discrete-time plants subject to persistent bounded disturbances. In the context of certain feedback objectives, it was shown that time-varying compensation offers no advantage over time-invariant compensation. These results complement similar results for feedback systems subject to finite-energy disturbances. It was shown that time-varying compensation does not improve the optimal rejection of persistent bounded disturbances. This result was obtained by exploiting a key observation that any time-varying compensator which yields a given degree of disturbance rejection must do so uniformly over time, thereby removing any advantage of time-variation. This key observation was used to show that time-varying compensation does not improve the optimal rejection of disturbances, regardless of the norm used to measure the disturbances. Thus, absolutely summable, finite-energy, or persistent bounded disturbances can be treated in the same manner. It was shown that time-varying compensation does not help in the bounded-input-bounded-output robust stabilization of time-invariant plants with unstructured uncertainty. In doing so, it was also shown that the small-gain theorem is both necessary and sufficient for the bounded-input-bounded-output stability of certain linear time-varying plants subject to unstructured linear time-varying perturbations.

Original languageEnglish (US)
Pages (from-to)2342
Number of pages1
JournalProceedings of the IEEE Conference on Decision and Control
Volume3
StatePublished - 1989
Externally publishedYes

ASJC Scopus subject areas

  • Chemical Health and Safety
  • Control and Systems Engineering
  • Safety, Risk, Reliability and Quality

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