Natural second-order observers for second-order distributed parameter systems

The aim of this manuscript is to present an alternative method for designing state observers for second-order distributed parameter systems without resorting to a first-order formulation. This method has the advantage of utilizing the algebraic structure that second-order systems enjoy with the obvious computational savings in observer gain calculations. The proposed scheme ensures that the derivative of the estimated position is indeed the estimate of the velocity component and to achieve such a result, a parameter-dependent Lyapunov function was utilized to ensure the asymptotic convergence of the state estimation error.

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