Parameterization of full-order PI observers in second-order linear systems

Based on the parametric solutions to a generalized second-order Sylvester equation, a parametric method to solve the design of full-order PI observers is proposed in second-order linear systems. This proposed method presents the parametric expressions for the feedback gain matrices and the left eigenvector matrix of the full-order PI observers. An illustrative example shows the effectiveness and simpleness of the proposed method.