COMPUTATION OF A LOWER BOUND OF Umax

This subsection compares the results obtained with the three methods proposed in chapter 5 (section 3.). A rough frequency gridding is first considered. The three methods are then evaluated around the critical frequency.

6.1.1 USE OF A ROUGH FREQUENCY GRIDDING

Table 10.1. /1 Lower bounds.

Method

fi lower-bound

critical frequency (rad/s)

1

1.869

6.821

2

1.302

6.547

1.748

7.880

1.966

9.95

The frequency gridding is chosen as a set of 30 points logarithmically spaced between 0.01 rad/s and 100 rad/s. The results are presented in the above table. It is especially worth emphasizing that methods (1) and (2) only detect a single peak, while the third method, which is based on Linear Programming, detects the two most critical peaks (these ones also appear in Figure 10.4).

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