## 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 language | English (US) |
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Pages (from-to) | 2342 |

Number of pages | 1 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

Volume | 3 |

State | Published - 1989 |

Externally published | Yes |

## ASJC Scopus subject areas

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