A novel linear matrix inequality (LMI) condition for the stability of the sampled-data fuzzy control system based on the Takagi-Sugeno fuzzy model is presented. Using the novel Lyapunov functional, the relaxed stability condition is presented for the sampled-data fuzzy control and represented in the LMI format. A simulation example is provided to verify the effectiveness of the proposed technique.Introduction: Recently, as the digital-based controller has been widely used in various real plants, the sampled-data control [1,2], which is the discrete-time control for analogue systems, has been regarded as one of the most important issues. Especially, in many sampled-data control techniques, the sampled-data fuzzy control using the Takagi-Sugeno (T-S) fuzzy model can be effectively applied in the nonlinear system and thus has attracted much attention [3][4][5][6][7].In the sampled-data fuzzy control, there are two important issues: (i) minimisation of the discretisation error and (ii) relaxation of the conservativeness of the stability condition. In the case of the first issue, the discretisation error is perfectly removed using the input-delay conversion [3][4][5] or the exact discrete-time fuzzy model [6,7]. However, some limitations still exist in the case of the second issue. The inputdelay conversion approach has a conservative condition derived from the input-delay system. Moreover, because the exact discrete-time fuzzy model is represented as the complex form, the stabilisation condition has the conservativeness.Motivated by the aforementioned analysis, this Letter proposes a novel linear matrix inequality (LMI) condition to relax the conservativeness of the stability condition for the sampled-data fuzzy control system. On the basis of the T-S fuzzy model, the sampled-data fuzzy controller is supposed, and the closed-loop system is obtained. Using the novel Lyapunov functional and the additional null term, the stability condition is presented, and its sufficient condition is derived into an LMI format. Finally, the validity of the proposed idea, technique and procedure are shown by comparison with the previous techniques in the simulation example.
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