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The parameter set of a linear parameter-varying system is divided into a number of subsets so that robust feedback gains may be designed for each subset of parameters. The concept of a quasi-invariant set is introduced, which allows finite steps of delay in re-entrance to the set. A positively invariant set with respect to a gain-scheduled state feedback control can be easily obtained from the quasi-invariant set. A constrained receding-horizon control algorithm that deploys degrees of freedom to steer the current state into a positively invariant set was developed. The proposed receding-horizon control method is formulated as linear programming and its computational load can be reduced significantly using a superposition technique.