Time-varying versus time-invariant compensation for rejection ofpersistent bounded disturbances and robust stabilization |
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Authors: | Shamma JS Dahleh MA |
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Affiliation: | Dept. of Electr. Eng., Minnesota Univ., Minneapolis, MN; |
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Abstract: | 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 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 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 |
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