Title :
A state-space approach to analysis of almost periodic nonlinear systems with sector nonlinearities
Author :
Seung Jean Kim ; In-Joong Ha
Author_Institution :
Sch. of Electr. Eng., Seoul Nat. Univ., South Korea
Abstract :
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.
Keywords :
Lyapunov methods; asymptotic stability; feedback; nonlinear control systems; periodic control; stability criteria; state-space methods; time-varying systems; Lyapunov approach; almost periodic nonlinear systems; circle criterion; feedback connection; linear system; sector nonlinearities; state-space approach; time-varying nonlinear element; time-varying nonlinearity; uniform asymptotic stability; Differential amplifiers; Differential equations; Feedback; Frequency conversion; Frequency modulation; Linear systems; Mixers; Nonlinear systems; Stability; Time varying systems;
Journal_Title :
Automatic Control, IEEE Transactions on
