Rational multiplier IQCs for uncertain time-delays and LMI stability conditions

This paper describes a set of delay-dependent IQC stability conditions for time-delay uncertainty. The IQC’s are linearly parameterized in terms of a pair of rational stability multipliers, each active over one of a pair of complementary frequency intervals. Using the finite-frequency positive real lemma, each of these finite-frequency IQC conditions are shown to be equivalent to a frequency-independent LMI condition, thereby dispensing with the need for frequency-sweeping. Keywords— Time-delay system, stability criteria, multiplier, robust control, IQC.