A dual formulation of mixed μ and on the losslessness of (D, G) scaling

Abstract

This paper studies the mixed structured singular value, /spl mu/, and the well-known (D,G)-scaling upper bound, /spl nu/. A dual characterization of /spl mu/ and /spl nu/ is derived, which intimately links the two values. Using the duals it is shown that /spl nu/ is guaranteed to be lossless (i.e. equal to /spl mu/) if and only if 2(m/sub r/+m/sub e/)+m/sub C//spl les/3, where m/sub r/, m/sub c/; and m/sub C/ are the numbers of repeated real scalar blocks, repeated complex scalar blocks, and full complex blocks, respectively. The losslessness result further leads to a variation of the well-known Kalman-Yakubovich-Popov lemma and Lyapunov inequalities.