Geometric stability criteria for certain non-linear time varying systems

Explicit geometric criteria for the exponential stability of a non-linear feedback system (consisting of a time-invariant block G in the forward path and a non-linear time varying gain φ.k(t) in the feedback path) are presented when φ(.) belongs to certain classes of non-linear functions. The resulting bound on $\text{(}\text{dk}\text{dt}\text{)}\text{k}$] is less stringent than those found in the literature.