Dynamic output-feedback control for singular interval-valued fuzzy systems: Linear matrix inequality approach

Abstract

This paper introduces an admissibilization condition for singular interval-valued fuzzy systems with a dynamic output-feedback controller using a linear matrix inequality approach. The derivation of the admissibility criterion (satisfying regularity, non-impulsiveness and stability) for the closed-loop system of the singular interval-valued fuzzy systems using the dynamic output-feedback controller is concerned. Here, the derived criterion is represented as the parameterized matrix inequalities depending on the membership functions of the system and the controller. To relax the derived parameterized matrix inequalities, this paper proposes a relaxation lemma based on the properties of the membership functions and their relations. By using this lemma, the parameterized matrix inequalities are converted into the matrix inequalities independent of the membership functions but not convex. Therefore, by introducing the structures of the variables and the congruent transformation matrix, a sufficient condition for the admissibility criterion is successfully given in terms of strict linear matrix inequalities. Two numerical examples are given to show the effectiveness of the proposed control.