| 内容提要: |
Positive realness is a fundamental property in linear circuit and system theory, which has many applications in various fields, such as realization theory of electric networks, the absolute stability analysis, and the inverse optimal control problem. This study mainly considers the positive realness of second-order and higher-order descriptor systems. Firstly, a necessary and sufficient condition for positive realness of second-order descriptor systems is given without any linearization. Based on the relations between positive realness and optimal control theory, the solutions of the positive real lemma can be represented by symmetric positive semi-definite matrices, which are derived by the solutions of a second-order generalized Riccati equation. Then, the extended strictly positive real lemma of higher-order descriptor systems is presented in terms of the original coefficient matrices of the system by applying some polynomial matrix decomposition techniques. Furthermore, linear matrix inequality conditions are determined for testing the positive realness and extended strictly positive realness of the system. |