The circle criterion and almost periodic inputs

We give a stability theorem concerning the response of systems to inputs th at are asymptotically almost periodic. We also apply our theorem to the gov erning integral equation of a large class of circuits containing a nonlinea r capacitor, We find that circuits for which a certain critical-disk condit ion is met are ap-stable in the sense that (a) small changes in the input r esult in small changes in the output and (b) the response to an asymptotica lly almost periodic input is an asymptotically almost periodic output whose almost periodic part does not depend on the transient part of the input, a nd the frequencies of the almost periodic part of the output have the prope rty that they are restricted to the set {omega : omega = Sigma(j=1)(q) k(j) omega(j); omega(j) epsilon k(j) Lambda, k(j) greater than or equal to 0 and q > 0 integers} where Lambda is the set of frequencies of the almost perio dic part of the input.