A new observer for Takagi–Sugeno fuzzy models and its applications

In this paper, a new discrete-time event-triggered mechanism (DTETM) is proposed, which is used in the framework of designing a discrete-time event-triggered observer (DTETO) for Takagi–Sugeno (T-S) fuzzy models with external disturbances. Existence conditions for the proposed DTETO are derived and formulated in terms of a convex optimization problem, which gives unknown observer matrices and minimized attenuation levels. Finally, an effective algorithm is obtained to estimate the state vector of the uncertain wind turbine system with a permanent magnet synchronous generator, the Chua’s circuits, and the Rossler chaotic system. Compared with the existing T-S fuzzy observers operated based on time-triggered mechanisms or periodic memory sampled-data mechanisms, which may lead to wasteful communication resources, the proposed approach in this paper uses a novel Zeno-free DTETM, which effectively reduces communication and estimation resource usage while ensuring the desired estimation performance. Moreover, unlike the existing discrete-time event-triggered T-S fuzzy observers and fuzzy filters, which are effective in estimating the state vectors of discrete-time fuzzy dynamic models, the one in this paper may be useful in estimating the state vectors of continuous-time fuzzy dynamic models.