Fuzzy Resilient $\mathcal {H}_\infty$ Filter Design for Continuous-Time Nonlinear Systems

In this article, the resilient
$\mathcal H_\infty$
filter design problem for continuous-time nonlinear systems is addressed. A Takagi–Sugeno fuzzy model with norm-bounded uncertainties is used to represent the nonlinear plant. Meanwhile, the fuzzy filter to be designed is assumed to have gain variations. A useful matrix inequality decoupling approach is proposed to separate the product terms with different types of uncertainties. Then, the resulting design condition of the resilient
$\mathcal H_\infty$
filter is described by strict linear matrix inequalities. Compared with the existing fuzzy resilient filtering results, the proposed design method shows a strong advantage of reducing design conservatism. Finally, a simulation example is provided to demonstrate the feasibility and the advantage of the proposed design method.