Nonfragile \(H_\infty\) filter design for nonlinear continuous-time system with interval time-varying delay (Q1629573)

Summary: This paper investigates nonfragile \(H_\infty\) filter design for a class of continuous-time delayed Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delays. Filter parameters occur multiplicative gain variations according to the filter's implementation, to handle this variations, a nonfragile \(H_\infty\) filter is presented and a novel filtering error system is established. The nonfragile \(H_\infty\) filter guarantees the filtering error system to be asymptotically stable and satisfies given \(H_\infty\) performance index. By constructing a novel Lyapunov-Krasovskii function and using Linear Matrix Inequalities (LMIs), delay-dependent conditions are exploited to derive sufficient conditions for nonfragile designing \(H_\infty\) filter. Using new matrix decoupling method to reduce the computational complexity, the filter parameters can be obtained by solving a set of LMIs. Finally, numerical examples are given to show the effectiveness of the proposed method.