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Robust dynamic output feedback fuzzy Lyapunov stabilization of Takagi-Sugeno systems – a descriptor redundancy approach. (English) Zbl 1176.93045
Summary: 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 \(H_{\infty }\) criterion in order to minimize the influence of external disturbances. Finally, a few academic examples illustrate the efficiency of the proposed approaches.

MSC:
93C42 Fuzzy control/observation systems
93D15 Stabilization of systems by feedback
93C15 Control/observation systems governed by ordinary differential equations
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