On the stability of a linear time-varying system

A single-loop linear system with a time-invariant stable block
G
in the direct path and a time-varying gain in the feedback path is analyzed for asymptotic stability in the Popov framework by way of admitting noncausal "multipliers" in the stability criterion. It is shown that an auto-correlation bound, analogous to O'Shea's cross-correlation bounds [1], results in a constraint on dk/dt more restrictive than that of Gruber and Willems [2].