Time-Varying Versus Time-Invariant Compensation for Rejection of Persistent Bounded Disturbances and Robust Stabilization

Jeff S. Shamma, Munther A. Dahleh

Research output: Contribution to journalArticlepeer-review

63 Scopus citations

Abstract

This paper considers time-varying compensation for linear time-variant discrete-time plants subject to persistent bounded disturbances. In the context of certain feedback objectives, it is shown that time-varying compensation offers no advantage over time-invariant compensation. These results complement similar existing results for feedback systems subject to finite-energy disturbances. First, it is shown that time-varying compensation does not improve the optimal rejection of persistent bounded disturbances. This result is 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 is further exploited 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 may be treated in the same manner. It is then 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 is 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)838-847
Number of pages10
JournalIEEE Transactions on Automatic Control
Volume36
Issue number7
DOIs
StatePublished - Jan 1 1991

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

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