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| Stability and Stabilization for Uncertain Fuzzy System with State Quantization Based on Sample-data Control |
| ZHAO Zhi-wei1,2,YANG Liu1,XIE Li-dian3,GE Chao1 |
1. Institute of Electrical Engineering, North China University of Science and Technology, Tangshan, Hebei 063210, China
2. College of Artificial Intelligence, Tangshan University, Tangshan, Hebei 063000, China
3. Shijiazhuang Haishan Industrial Development Corporation, Shijiazhuang, Hebei 050200, China |
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Abstract The stability and stabilization problems of the T-S fuzzy system with uncertainty and state quantization were studied. Considering that fuzzy membership functions (FMFs) are the main characteristic of T-S fuzzy model, if the information about FMFs is not added, it will be conservative. So, a novel Lyapunov-Krasovskii functional (LKF) which contained not only the information of state variables but also FMFs was constructed. Besides, the states on both sides of the sampling interval were incorporated into LKF. When deriving LKF, the product terms which consisted of derivative of FMFs and LKF coefficient were involved. And the product terms were discussed to ensure their negative definition. Later, enough stability conditions were expressed in the form of linear matrix inequalities (LMIs). The maximum sampling intervals and controller parameters were solved by MATLAB toolbox with the optimal parameters. Finally, a numerical example was simulated, and the maximum sampling interval for the T-S fuzzy inverted pendulum system was increased to 0.040s.
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Received: 22 September 2020
Published: 23 March 2022
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2022, Vol. 43 
