Generalized PI Observer Design for Higher-order Descriptor Linear Systems

Based on the solutions of a class of higher-order Sylvester matrix equations, a parametric method for the proportional-integral (PI) observer design problem of higher-order descriptor linear systems is proposed. The parametric expressions for the gain matrices and the left eigenvector matrix of the kind of observer are given. The original system coefficient matrices are utilized and manipulations are involved only in high-dimensional matrices. A numerical case demonstrates the effect of the proposed method.