A piecewise affine control Lyapunov function for robust control

Ngoc Anh Nguyen 1 Sorin Olaru 2, 1
2 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 : This paper presents the construction of a convex piecewise affine control Lyapunov function for constrained linear discrete-time systems, affected by bounded additive disturbances. Exploiting the properties of this control Lyapunov function, the closed-loop dynamics are shown to converge to a given full-dimensional robust positively invariant set. Moreover, the proposed method leads to a simple robust control algorithm which only requires solving a linear programming problem at each sampling instant. Finally, the controller design is illustrated via a numerical example.
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Ngoc Anh Nguyen, Sorin Olaru. A piecewise affine control Lyapunov function for robust control. 16th European Control Conference (ECC 2018), Jun 2018, Limassol, Cyprus. ⟨hal-01720263⟩

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