论文标题
协方差扩展方程：一种分析插值的Riccati型方法
The Covariance Extension Equation: A Riccati-type Approach to Analytic Interpolation
论文作者
论文摘要
合理性和衍生性约束的分析插值问题在系统和控制中无处不在。本文基于非标准的Riccati-Type方程，在标量和矩阵情况下为此类问题提供了一种新方法。溶液矩阵的等级与插值的程度相同，因此提供了自然的模型还原方法。提出了一种同质延续方法，并将其应用于建模和稳健控制方面的一些问题。我们还解决了有关Kalman最初提出的协方差序列的正面程度的问题。
Analytic interpolation problems with rationality and derivative constraints are ubiquitous in systems and control. This paper provides a new method for such problems, both in the scalar and matrix case, based on a non-standard Riccati-type equation. The rank of the solution matrix is the same as the degree of the interpolant, thus providing a natural approach to model reduction. A homotopy continuation method is presented and applied to some problems in modeling and robust control. We also address a question on the positive degree of a covariance sequence originally posed by Kalman.
