稀疏关联不确定性系统的鲁棒稳定性分析
Robust Stability Analysis of Sparsely Interconnected Uncertain Systems
摘要：
本文研究稀疏关联不确定性系统的鲁棒稳定性分析。通过对具有积分二次约束的子系统之间的关联建模，我们证明了此类系统的鲁棒稳定性分析可以通过求解一组稀疏线性矩阵不等式来进行。我们还表明，稀疏制定的分析问题是等价的鲁棒性分析问题的经典配方，因此不引入任何额外的保守性。稀疏制定的分析问题，使我们能够应用依赖于有效的稀疏分解技术的方法，我们的数值结果表明，这种方法的有效性相比，是基于标准制定的分析问题的方法。
英文摘要：
In this paper, we consider robust stability analysis of large-scale sparsely interconnected uncertain systems. By modeling the interconnections among the subsystems with integral quadratic constraints, we show that robust stability analysis of such systems can be performed by solving a set of sparse linear matrix inequalities. We also show that a sparse formulation of the analysis problem is equivalent to the classical formulation of the robustness analysis problem and hence does not introduce any additional conservativeness. The sparse formulation of the analysis problem allows us to apply methods that rely on efficient sparse factorization techniques, and our numerical results illustrate the effectiveness of this approach compared to methods that are based on the standard formulation of the analysis problem.
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