Minimality for uncertain systems and IQCs

A necessary and sufficient condition is presented for the minimality of uncertain systems represented by a linear fractional transformation (LFT) on repeated scalar time-varying operators. This condition generalizes the role of controllability and observability gramians, and is expressed in terms of singular solutions to a pair of linear matrix inequalities (LMIs). Previous results on S-procedure losslessness for integral quadratic constraints (IQCs) play a key role in these results.<
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