Necessary and Sufficient Conditions for Stabilizing an Uncertain Stochastic Multidelay System
研究了离散时间随机系统中存在模型不确定性和多个输入时滞时的均方渐近稳定问题，提出了基于矩阵齐次多项式的充要稳定判据，并给出了时滞裕度的闭式表示。
We focus on the problem of asymptotically mean-square stabilization in discrete-time stochastic systems that exhibit plant uncertainty, multiple input delays, and multiplicative noises. Our innovative contributions are described as follows. First, we employ a reduction method to transform the original model into a delay-free auxiliary system, and establish an equivalent proposition for stabilization based on this reformulation. On the basis of the reformulated model, we propose two stabilization criteria for the uncertainty-free case, including both Lyapunov-type and Riccati-type criteria. More generally, we extend the stabilization result to the uncertain model, and propose a necessary and sufficient stabilization criterion utilizing matrix homogeneous polynomials. Finally, we explore the existence and uniqueness of a delay margin under certain structural restrictions, and provide a closed-form representation of this margin.