This paper characterizes the robust second-moment stability of stochastic linear systems subject to varying delays. The delays assume a particular form suitable to represent packet loss in networked control systems, under the zero-order hold feedback. The proposed robust stability condition requires checking the spectral radius of an appropriate matrix that that depends on uncertain parameters belonging to a polytope. Due to this polytope’s dependence, checking the spectral radius is difficult from the numerical viewpoint. As an attempt to solve the problem, we convert the polytope-based condition into a randomized approach. Namely, we present probability bounds that help us certificate the robust second-moment stability under high probability. A real-time electronic application illustrates the potential benefits of our approach.

本文描述了受不同延迟影响的随机线性系统的稳健二阶矩稳定性。在零阶保持反馈下，延迟采用适合表示网络控制系统中数据包丢失的特定形式。建议的稳健稳定性条件需要检查取决于属于多胞体的不确定参数的适当矩阵的谱半径。由于这种多胞体的依赖性，从数值角度检查光谱半径是困难的。为了解决这个问题，我们将基于多面体的条件转换为随机方法。也就是说，我们提出了概率界限，帮助我们证明高概率下的稳健二阶矩稳定性。实时电子应用程序说明了我们方法的潜在好处。