Stochastic output feedback control: Convex lifting approach

This paper presents a method to design output feedback control for discrete-time linear systems, affected by bounded additive state, output disturbances, and subject to chance constraints on the state and hard constraints on the control input. This method relies on a so-called convex lifting which is a nonnegative, convex, piecewise affine function, equal to 0 over a given stochastic positively invariant set and strictly positive outside this set. Accordingly, it is shown that this function is strictly decreasing along the closed-loop dynamics outside this invariant set and convergent to 0 as time tends to infinity. Consequently, the state is convergent to the given invariant set, while the method only requires solving a linear program at each sampling instant.