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首页> 外文期刊>IEEE Transactions on Automatic Control >A Unified Framework for Deterministic and Probabilistic -Stability Analysis of Uncertain Polynomial Matrices
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A Unified Framework for Deterministic and Probabilistic -Stability Analysis of Uncertain Polynomial Matrices

机译：确定性和概率的统一框架-不确定多项式矩阵的稳定性分析

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摘要

In control theory, we are often interested in robust D-stability analysis, which aims at verifying if all the eigenvalues of an uncertain matrix lie in a given region D. Although many algorithms have been developed to provide conditions for an uncertain matrix to be robustly D-stable, the problem of computing the probability of an uncertain matrix to be D-stable is still unexplored. The goal of this paper is to fill this gap in two directions. First, the only constraint on the stability region D that we impose is that its complement is a semialgebraic set. This comprises many important cases in robust control theory. Second, the D-stability analysis problem is formulated in a probabilistic framework, by assuming that only few probabilistic information is available on the uncertain parameters, such as support and some moments. We will show how to compute the minimum probability that the matrix is D-stable by using convex relaxations based on the theory of moments.
机译：在控制理论中，我们经常对鲁棒的D稳定性分析感兴趣，该分析旨在验证不确定矩阵的所有特征值是否都在给定区域D中。尽管已经开发了许多算法来为不确定矩阵提供鲁棒的条件D稳定，计算不确定矩阵为D稳定的概率的问题仍未解决。本文的目标是从两个方向填补这一空白。首先，我们对稳定性区域D施加的唯一约束是其补码是半代数集。这包括鲁棒控制理论中的许多重要情况。其次，通过假设关于不确定参数（例如支持和某些时刻）的可用概率信息很少，在概率框架中提出了D稳定性分析问题。我们将展示如何基于矩理论通过使用凸松弛来计算矩阵是D稳定的最小概率。

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