A Set-Theoretic approach to solving control problems is presented for systems with control and state constraints which are subjected to input disturbances. The input disturbance is modeled as an unknown-but-bounded process. The constraints on the states and controls are treated explicitly. The primary objective is to construct a control system that uses only available control effort to insure nonviolation of the prespecified state constraints in the presence of the input disturbance. Since the constraints are treated directly, this technique yields a design that satisfies the constraints. The effectiveness of Set-Theoretic control synthesis is evaluated by means of an example and by comparison with a specific Linear-Quadratic Control design procedure.

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