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 motivates us to introduce and analyze Mean-$q$-Power stability criterion, generalizing the mean-square stability criterion, and then juxtapose these techniques to other, classic tools in control.

翻译：受水力学及建筑中温控负荷网络应用的启发，本文研究了由加性噪声和一般位置乘性噪声驱动的线性动力系统控制问题。利用随机乘性过程的数学理论，我们提出了一种估计状态向量概率分布肥厚代数尾的通用方法。这促使我们引入并分析平均q次幂稳定判据（推广了均方稳定判据），并将其与控制领域其他经典工具进行对比。