Invariant Sets for Discrete-Time Constrained Linear Systems using a Sliding Mode Approach

Invariant set theory has been recognized as an important tool for control design of constrained systems subject to disturbances. Indeed, invariant sets as the minimal robustly positively invariant set help verify whether constraints are satisfied in closed-loop. This paper studies a class of discrete-time linear systems under additive disturbances. We propose a method to compute the linear state feedback gain that minimizes the impact of disturbances, related to the mRPI, on the constrained closed-loop dynamics. The method relies on the solution of an optimization problem that is formulated using set-theoretic methods and discrete-time sliding mode parametrization.