Kronecker权重用于Markov跳跃线性系统的不稳定性分析
Kronecker weights for instability analysis of Markov jump linear systems
AI总结：
本文提出了一种新的指数均值不稳定性准则，通过构建辅助Markov跳跃线性系统和Kronecker积矩阵权重，实现对Markov跳跃线性系统不稳定性更精确的分析。
摘要：
本文分析了连续时间Markov跳跃线性系统的不稳定性。尽管已存在多种有效的稳定性判据，但缺乏验证其不稳定的 方法。本文提出了一种新的指数均值不稳定性判据。分析的主要工具是一个辅助Markov跳跃线性系统，该系统由给定系统矩阵与一组适当矩阵权重的Kronecker积构成。我们进一步表明，寻找更紧的不稳定性分析矩阵权重的问题可以转化为一个仿射矩阵族的谱优化问题，这可以通过基于梯度的非光滑优化算法高效解决。通过数值示例验证了所提方法的有效性。
英文摘要：
In this paper, we analyze the instability of continuous-time Markov jump linear systems. Although there exist several effective criteria for the stability of Markov jump linear systems, there is a lack of methodologies for verifying their instability. In this paper, we present a novel criterion for the exponential mean instability of Markov jump linear systems. The main tool of our analysis is an auxiliary Markov jump linear system, which results from taking the Kronecker products of the given system matrices and a set of appropriate matrix weights. We furthermore show that the problem of finding matrix weights for tighter instability analysis can be transformed to the spectral optimization of an affine matrix family, which can be efficiently performed by gradient-based non-smooth optimization algorithms. We confirm the effectiveness of the proposed methods by numerical examples.
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