Robust dynamic output feedback fuzzy Lyapunov stabilization of Takagi–Sugeno systems—A descriptor redundancy approach

Abstract

This paper deals with Takagi–Sugeno (T–S) systems stabilization based on dynamic output feedback compensators (DOFC). In fact, only few results consider DOFC for T–S systems and most of them propose quadratic Lyapunov functions to provide stability conditions, which may lead to conservatism. In this work, to overcome this drawback and to enhance the closed-loop transient response, we provide for T–S uncertain closed-loop systems non-quadratic stability conditions. Based on a fuzzy Lyapunov candidate function and the descriptor redundancy property, these stability conditions are written in terms of linear matrix inequalities (LMI). Afterward, the DOFC is designed with H ∞ criterion in order to minimize the influence of external disturbances. Finally, a few academic examples illustrate the efficiency of the proposed approaches.