-stability of linear time-varying systems--Conditions involving noncausal multipliers

New criteria in the multiplier form are presented for the input-output stability in the L2-space of a linear system with a time-varying element in a feedback loop. These are sufficient conditions for the system stability and involve conditions on the shifted imaginary-axis behavior of the multipliers. The criteria permit the use of noncausal multipliers, and it is shown that this necessitates to be bounded from above as well as from below. The method of derivation draws on the theory of positivity of compositions of operators and time-varying gains, and the results are shown to be more general than the existing criteria.