Stabilizing predictive control with output feedback for asymptotic tracking

A multivariable state space formulation of the GPC (generalized predictive control) law that can be implemented using output feedback is derived. This is done by using a particular nonminimal state space model where the current state is completely known. Sufficient conditions for stability of closed loop systems that result from implementing solutions of the finite horizon LQ problem for arbitrary fixed costing horizons are then presented. On this basis, a class of predictive control laws that ensures stability of the closed loop system is proposed. When the plant is required to track a known reference signal with step changes, a predictive output feedback controller that preserves stability of the closed loop system and achieves asymptotic tracking of the reference signal is derived.