ABSTRACT

In this work, we study the parametric Sylvester matrix equation $A\left(p\right)X+XB\left(p\right)=C\left(p\right)$ whose elements are linear functions of uncertain parameters varying within some intervals. We first explore some properties of its solution set and then present some sufficient conditions for boundedness of the solution set. The main work is developing a modified variant of the parametric Krawczyk operator which reduces the computational complexity of enclosing the solution set significantly, compared to the parametric Krawczyk operator on the Kronecker product form. Some numerical experiments are given to illustrate the effectiveness of the proposed method.

摘要

在这项工作中，我们研究了参数 Sylvester 矩阵方程$\mathrm{一个}\left(p\right)X+X乙\left(p\right)=C\left(p\right)$其元素是在一定区间内变化的不确定参数的线性函数。我们首先探索其解集的一些性质，然后给出解集有界的一些充分条件。主要工作是开发参数 Krawczyk 算子的修改变体，与 Kronecker 乘积形式上的参数 Krawczyk 算子相比，它显着降低了封闭解集的计算复杂性。给出了一些数值实验来说明所提方法的有效性。