  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.
