Improved Output Feedback Control of Constrained Linear Systems using Invariant Sets

We propose an improved design method for output feedback control of discrete-time linear systems subject to state and control constraints, additive disturbances and measurement noise. Output Feedback Controlled-Invariant polyhedral sets are used to ensure that state and input constraints are satisfied all time. The control strategy seeks to enforce the set of states consistent with the measured output into a closed ball around the origin. The control input is computed through the solution of Linear Programming (LP) problems, whose goal is to minimize the size of the ball one step ahead. Then, we use the optimization results to reduce the set of admissible states, steering the state to a smaller ball around the origin. The improvement provided by the proposed strategy is illustrated by numerical examples.