Guaranteed cost inequalities for robust stability and performance analysis

The shifted bounded real bound, the shifted linear bound, the shifted inverse bound, and the shifted Popov bound are considered. These bounds are compared with the bounded real bound, the linear bound, the inverse bound, the Popov bound and a LMI (linear matrix inequality) bound. It is shown that these shifted bounds can by recast as LMIs, and presented as guaranteed cost inequalities. For several examples, it is shown that the shifted bounded real bound and shifted inverse bound exhibit comparable performance to that of the best possible parameter-independent bound. It is shown for several numerical examples that the shifted Popov bound, which is a parameter-dependent bound, may be less conservative than parameter-independent bounds