The circle criterion and almost periodic inputs

摘要

We give a stability theorem concerning the response of systems to inputs that are asymptotically almost periodic. We also apply our theorem to the governing integral equation of a large class of circuits containing a nonlinear capacitor. We find that circuits for which a certain critical-disk condition is met are ap-stable in the sense that (a) small changes in the input result in small changes in the output and (b) the response to an asymptotically almost periodic input is an asymptotically almost periodic output whose almost periodic part does not depend on the transient part of the input, and the frequencies of the almost periodic part of the output have the property that they are restricted to the set {ω:ω=Σj=1qkjω j;ωj∈Λ, kj⩾0 and q>0 integers} where h is the set of frequencies of the almost periodic part of the input