Abstract
In the study of adaptive parameter identification, the parameter error dynamics resulting from the gradient algorithm represents a very special class of parametrically excited system, whose stability condition has been studied thoroughly. By utilizing this stability condition, one can develop a new active control design for a parametrically excited system which exhibits sustained but bounded oscillations due to the time-varying system matrix. The resultant observer-based state feedback control guarantees exponential decay of the state oscillation given that the system is both uniformly controllable and uniformly observable. The advantage of the proposed design is that it requires neither information of time derivatives of the parametric excitations, nor predicting future information of the parametric excitations.
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