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：受流体力学及建筑温控负荷网络应用的启发，本文研究了一类由一般性加性和乘性噪声驱动的线性动力系统的控制问题。利用随机乘性过程的数学理论，我们提出了一种普适性方法，用以估计状态向量概率分布的肥厚代数尾部。这促使我们引入并分析均值-q-幂稳定性准则（Mean-$q$-Power stability criterion），该准则是对均方稳定性准则的推广，随后我们将这些方法与其他经典控制工具进行了对比研究。