A state-space approach to analysis of almost periodic nonlinear systems with sector nonlinearities

The nonlinear system considered in this paper consists of two components—a linear system and a time-varying nonlinear element in the feedback connection—and is almost periodic. It is shown using a state-space approach (or Lyapunov approach) that if the well-known circle criterion is satisfied, then there exists an almost periodic solution which is uniformly asymptotically stable in the large. Furthermore, it is also shown that the spectra of the almost periodic solution can be characterized by those of the input and the time-varying nonlinearity.