Abstract
Abstract Invariant set theory has been recognized as an important tool for control design of constrained systems subject to disturbances. Indeed, for a given control law, entering an invariant set guarantees recursive state and input constraint satisfaction in closed-loop. This paper focuses on discrete-time linear systems subject to bounded matched additive disturbance. The problem of the joint synthesis of control laws and associated invariant sets that are optimized with regards to the state constraints is investigated. An interpolation method is used to enlarge the controllable region.
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