Robust stability with time-varying structured uncertainty

Considers the problem of assessing robust stability in the presence of block-diagonally structured time-varying dynamic uncertainty. It is shown that robust stability holds only if there exist constant scalings which lead to a small gain condition. The notion of stability here is finite-gain stability over finite-energy signals. In sharp contrast to the case of time-invariant dynamic uncertainty, this result is not limited by the number uncertainty blocks. These results parallel previous results regarding finite-gain stability over persistent bounded signals