Converse Schwarz inequality and an instability-related property of feedback systems

The converse of Schwarz inequality is applied to the analysis of an instability-related property (hereafter called Property P) of feedback systems. For systems containing a linear time invariant part with a non-linear (time varying) gain in the feedback path, the conditions for the Property P to hold are given ill ‘ multiplier ’ form; for more general systems, these conditions are expressed in terms of the passivity and finite gains of certain operators derived from the system (forward and feedback) operators.