$H_\infty $ Stabilization for Sampling Fuzzy Systems With Asynchronous Constraints on Membership Functions

This paper investigates the problem of <inline-formula> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> stabilization for nonuniform sampling fuzzy systems. To achieve better performance, a parallel distributed compensation scheme is proposed to design a nonlinear controller. By taking the deviation bounds of asynchronous normalized membership functions into account, the <inline-formula> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> stability criterion is first obtained, which is dependent on the deviation bounds of asynchronous normalized membership functions. To reduce the computational complexity, a method for eliminating slack variables and a structured vertex separator for reducing the number of linear matrix inequalities are provided, and then an <inline-formula> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> stabilization criterion with less complexity and less conservatism is obtained. Finally, an illustrative example is given to show the effectiveness of the proposed method and the significant improvement on the existing results.