Motivated by applications in hydrodynamics and networks of thermostatically-control loads in buildings we study control of linear dynamical systems driven by additive and also multiplicative noise of a general position. Utilizing mathematical theory of stochastic multiplicative processes we present a universal way to estimate fat, algebraic tails of the state vector probability distributions. This prompts us to introduce and analyze mean-q-power stability criterion, generalizing the mean-square stability criterion, and then juxtapose it to other tools in control.

翻译：受流体动力学及建筑中恒温控制负载网络应用的启发，我们研究了一般加性和乘性噪声驱动的线性动力系统的控制问题。利用随机乘法过程的数学理论，我们提出了一种估算状态向量概率分布中厚代数尾部的普适方法。这促使我们引入并分析了均值q次幂稳定性判据（该判据推广了均方稳定性判据），并将其与控制领域的其他工具进行了对比。