A predictive controller robust against persistent disturbances is presented for discrete-time linear time-invariant constrained systems. It is known that the action of a bounded disturbance on a nominally designed predictive control loop can affect feasibility and consequently produce a dramatic degradation of performance: in certain cases even an unbounded state behaviour can occur. To overcome this difficulty, the notion of controlled disturbance (cd) invariant set has been used. The proposed controller is based on constrained optimization of a nominal (disturbance-free) performance index with the additional constraint that the future state will lie in a prescribed cd-invariant set whatever disturbance may have occurred. As a result, both bounded-disturbance-bounded-state stable behaviour and constraint fulfillment are guaranteed.
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