Exponential stabilization of sampled-data fuzzy systems via a parameterized fuzzy Lyapunov-Krasovskii functional approach

Abstract

This paper devotes to stabilize nonlinear systems based on Takagi-Sugeno (T-S) fuzzy models, where only sampled state is available. Note that the membership functions (MFs) between T-S fuzzy models and fuzzy controllers are asynchronous under a sampling mechanism, a fuzzy state feedback controller with asynchronous MFs is introduced. A new parameterized fuzzy Lyapunov-Krasovskii functional (PFLKF) approach is presented to ensure that the closed-loop system is exponentially stable and there exists a large well-defined domain of attraction. In general, it is difficult to compute in advance the upper bounds of the time derivatives of MFs, where these time derivatives appear in the time derivative of the PFLKF or the errors of the asynchronous MFs. To this end, a novel quadratic inequality is established to characterize the time derivatives of MFs. Then an MF-dependent exponential stability criterion is given in terms of linear matrix inequalities, and a co-design method for the controller gains and the domain of attraction is presented. Finally, three illustrative examples show the effectiveness and advantages of the proposed approach.