Stabilization Criteria for T–S Fuzzy Systems With Multiplicative Sampled-Data Control Gain Uncertainties
K. Subramanian, Young Hoon Joo
Abstract
This study concerns the stabilization criteria of Takagi–Sugeno (T–S) fuzzy systems under the memory-based sampled-data control. Contrasted to the traditional sampled-data control strategy, a more general control scheme that admits the signal transmission delay and the multiplicative control gain uncertainties is designed. In order to indicate the perturbations of control gain, the Bernoulli sequence is applied to the designed control scheme. At the same time, the membership function dependent <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> performance index is introduced to attenuate the disturbances of continuous-time T–S fuzzy systems for the first time. By utilizing the novel <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> performance index together with the appropriate Lyapunov–Krasovskii functional, including the information of sampling period and signal transmission delay, the sufficient conditions are derived in the framework of linear matrix inequalities. These conditions ensure the stabilization of concerned T–S fuzzy systems and enlarging the maximum sampling period. At last, the advantages of the derived results are shown by the numerical examples.