The scaled Popov criterion and bounds for the real structured singular value

A generalization of the multivariable Popov criterion is stated for norm-bounded, block-structured real matrices in the feedback path representing constant real parameter uncertainty for a nominal plant. This criterion is rendered less conservative by including scaling matrices whose structure is determined by the block structure of the uncertainty. The scaled Popov criterion is then used to derive an upper bound for the structured singular value for real parameter uncertainty. This upper bound is then rewritten in the form of a linear matrix inequality to facilitate numerical computation. Several numerical examples are given to illustrate the effect of the scaling matrices