基于多项式级数法的线性时变系统的结构分析

Structure Analysis of Time Varying Linear Systems via Polynomials Series

采用多项式级数变换法对时变线性系统的结构性质，主要是能观性、能控性进行了初步研究．对于多项式展开后得到的近似系统———ｍ级数值模型，给出了相应的不能观、能观、能控的定义及状态转移系数阵的概念；并且得到了在这种定义下，近似系统在某点的可观性、可控性和原时变系统在这点可观性、可控性之间的关系，从而说明进一步运用多项式展开后的系数阵来判别原时变线性系统的能观性。

The use of non orthogonal polynomials series(Taylor series) to analysis the structure of time varying linear systems is investigated, especially to the observability and controllability. The definitions of observability and controllability to system that is approximated with the help of Taylor series are given, and the concept of state transition coefficient matrix is also proposed. Applying these definitions the relations about controllability and observability between original time varying system and approximated system are obtained. These results can be used to test observability, controllability and stability and so on in terms of the coefficient matrices of the Taylor series expansion.