Robustness analysis for time-varying systems

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