A Filtered Transformation via Dynamic Matrix to State and Parameter Estimation for a Class of Second Order Systems

The problem of state and parameter estimation for a class of second-order time-varying systems is addressed in this paper. Two classes of estimators are designed for the system under different observability assumptions. The design procedure is based on a filtered transformation via dynamic matrix. The dynamic of the matrix is derived using the Immersion and Invariance technique. Adaptive parameter convergence is guaranteed under a weaker condition than traditional persistency of excitation, called non-square-integrability condition. The proposed estimator is shown to be applicable to the input voltage and current estimation from the output voltage of the AC-DC boost converter.