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

Nathan Michel 1, 2 Sorin Olaru 3, 1 Giorgio Valmorbida 1 Sylvain Bertrand 2 Didier Dumur 1
3 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
Abstract : 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 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 sliding mode control.
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Nathan Michel, Sorin Olaru, Giorgio Valmorbida, Sylvain Bertrand, Didier Dumur. Invariant Sets for Discrete-Time Constrained Linear Systems Using Sliding Mode Approach. 16th European Control Conference (ECC 2018), Jun 2018, Limassol, Cyprus. pp.2929-2934, ⟨10.23919/ECC.2018.8550119⟩. ⟨hal-01718460⟩

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