Open AccessStability and L2-Norm Bound Conditions for Takagi-Sugeno Descriptor Systems
Author(s) -
Benoît Marx,
José Ragot
Publication year - 2008
Publication title -
hal (le centre pour la communication scientifique directe)
Language(s) - English
Resource type - Conference proceedings
DOI - 10.3182/20080706-5-kr-1001.0563
Subject(s) - norm (philosophy) , computer science , control theory (sociology) , stability (learning theory) , upper and lower bounds , mathematics , artificial intelligence , control (management) , mathematical analysis , machine learning , epistemology , philosophy
International audienceIn 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