Controller Design for Discrete-Time Descriptor Models: A Systematic LMI Approach

Víctor Estrada Manzo (1) , Zsofia Lendek (2) , Thierry-Marie Guerra (1) , Philippe Pudlo (1)

1 LAMIH - Laboratoire d'Automatique, de Mécanique et d'Informatique industrielles et Humaines - UMR 8201
2 Technical University of Cluj-Napoca

This paper provides a systematic way to generalize the controller design for discrete-time nonlinear descriptor models. The controller synthesis is done using a Takagi-Sugeno representation of the descriptor models and linear matrix inequalities. We propose approaches to exploit the discrete-time nature of the problem by using delayed Lyapunov functions, which allow delayed controller gains. In addition, the well-known Finsler's Lemma is used to avoid the explicit substitution of the closed-loop dynamics. Examples are provided to show the effectiveness of the proposed results.

Mots clés: "Lyapunov methods"; "Delays"; "Indexes"; "Computational modeling"; "Systematics"; "Mechanical systems"; "Linear matrix inequalities"

Domaines: Automatique / Robotique

Víctor Estrada Manzo, Zsofia Lendek, Thierry-Marie Guerra, Philippe Pudlo. Controller Design for Discrete-Time Descriptor Models: A Systematic LMI Approach. IEEE Transactions on Fuzzy Systems, 2015, 23 (5), pp.1608-1621. ⟨10.1109/TFUZZ.2014.2371029⟩. ⟨hal-03428906⟩