  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.

Systems and Control