Output-Feedback Controlled-Invariant Polyhedra for Constrained Linear Systems

A design method is proposed for output-feedback control of linear systems subject to state and control constraints, additive disturbances and measurement noise. First, necessary and sufficient conditions for a polyhedral set to be controlled-invariant under output-feedback are presented, which can be checked by the solution of a set of Linear Programming problems. Then, a dynamic output-feedback compensator structure is proposed to guarantee constraint satisfaction, through the construction of an output-feedback controlled-invariant set, from a pair composed by a conditioned-invariant and a controlled-invariant polyhedron. Based on the available measurements and on the state of the compensator, a suitable control sequence can be computed to enforce the state constraints. Differently from other approaches, the proposed method does not rely on pre-computed linear controllers or observers. Therefore, it is likely to provide a solution for larger amplitudes of disturbances and noise, and larger uncertainties on the initial state, as illustrated by numerical examples.