PI Observer Design in Second-order DLS

A kind of proportional-integral (PI) observer for second-order descriptor linear system (DLS) is introduced. A parametric method for the observer design problem is presented based on the general solution to second-order Sylvester matrix equation (SME). This method not only provides the parametric expressions of the gain matrices and the corresponding finite left eigenvector matrix, but also ensures the regularity and impulse-freeness of the expanded error system. A numerical example is given to explain the process and clarify the effectiveness of the proposed method.