Exponential Stability, Semistability, and Boundedness of a Multi-ANF System

Abstract

A nonlinear system being composed of multiadaptive notch filters in parallel is introduced to track the sinusoidal components of an almost periodic signal and estimate their frequencies and amplitudes. An almost periodic nonlinear dynamic system for estimation of frequencies is achieved after the existence of a slow integral manifold is proved and results in a nonlinear autonomous system with averaging method employed. Three types of local stability of the autonomous system, the exponential stability in isolated equilibrium point and the semistability on center manifold and the ultimate boundedness under unknown periodic disturbance, are respectively investigated. The transient performance is affected by frequency adaptive gain independent of bandwidth parameter. The validity of the proposed algorithm is verified by simulation results.