Positivity Preservation Properties of the Rantzer Multipliers

The Rantzer multipliers are known to preserve the positivity of certain aberrations of memoryless monotone positive nonlinearities. We show that if the nonlinearity input is constrained to be positive valued for all time instants, these multipliers are positivity preserving for a larger class of nonlinearities. As a result, it follows that the Rantzer multipliers are useful in reducing the conservatism inherent in the multiplier theoretic stability analysis of feedback systems featuring a larger class of nonlinearities than the one these multipliers were originally intended for, so long as the nonlinearity input is positive-valued for all time instants.