论文标题
多变量状态空间系统及其相关系统矩阵的Fiedler线性化
Fiedler Linearizations of Multivariable State-Space System and its Associated System Matrix
论文作者
论文摘要
线性化是计算基质多项式特征值和特征向量的标准方法。在过去的十年中，为了处理代数结构并为了构建有效的数值方法而开发了各种线性化方法。矩阵多项式的线性化的重要来源是所谓的fiedler铅笔，这是Frobenius伴随形式的概括，并且这些线性化已扩展到常规的理性矩阵函数，这是[1，6]中LTI状态空间系统的传递函数。我们考虑一个多变量状态空间系统及其关联的系统矩阵S（λ）。我们介绍了S（λ）的Fiedler铅笔，并描述了其构造的算法。我们表明，Fiedler铅笔是系统矩阵S（λ）的线性化。
Linearization is a standard method in the computation of eigenvalues and eigenvectors of matrix polynomials. In the last decade a variety of linearization methods have been developed in order to deal with algebraic structures and in order to construct efficient numerical methods. An important source of linearizations for matrix polynomials are the so called Fiedler pencils, which are generalizations of the Frobenius companion form and these linearizations have been extended to regular rational matrix function which is the transfer function of LTI State-space system in [1, 6]. We consider a multivariable state-space system and its associated system matrix S(λ). We introduce Fiedler pencils of S(λ) and describe an algorithm for their construction. We show that Fiedler pencils are linearizations of the system matrix S(λ).
