Stability and L2-Norm Bound Conditions for Takagi-Sugeno Descriptor Systems

Benoît Marx (1) , José Ragot (1)

1 CRAN - Centre de Recherche en Automatique de Nancy

In this paper, the stability of Takagi-Sugeno (TS) descriptor systems is studied. In most of previous works concerning TS descriptor systems, the authors claimed that the study of polytopic matrix pencil reduces to the study of an augmented polytopic matrix pencil with a common matrix E. The approach they have used is based on a state augmentation. In this paper, it is proved that this transformation introduces impulsive terms, because time derivate of the state variables are added in the state vector. The major contribution of this paper is to avoid this state augmentation. A new sufficient stability condition is established. Stability with guaranteed decay rate and L2-norm bound are also studied. All results are given in the linear matrix inequality formalism.

Mots clés: stability analysis; Takagi-Sugeno systems; Singular systems

Domaines: Automatique / Robotique

Benoît Marx, José Ragot. Stability and L2-Norm Bound Conditions for Takagi-Sugeno Descriptor Systems. 17th IFAC World Congress, Jul 2008, Seoul, South Korea. pp.9976-9981, ⟨10.3182/20080706-5-KR-1001.0563⟩. ⟨hal-00319971⟩