Universality and Control of Fat Tails

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.