State and Parameter Estimation Based on Filtered Transformation for a Class of Second-Order Systems

This paper addresses the problem of state and parameter estimation for a class of second-order systems with single output. A new filtered transformation is proposed for the system via dynamic vector and matrix. In this method, the dynamics of the vector and matrix are derived by immersion and invariance technique such that the state estimation condition is guaranteed. Compared to the classical approaches that persistency of excitation (PE) condition is required for parameter convergence, the proposed method needs a weaker one, so called non-square-integrability condition, in the transformation via dynamic matrix. Simulation results are concluded for a class of regressors which are not PE but satisfy the new condition.