An LMI approach to the H∞ filter design for uncertain systems with distributed delays

This paper investigates the problem of robust H_∞ filter design for linear distributed delay systems with norm-bounded time-varying parameter uncertainties. The distributed delays are assumed to appear in both the state and measurement equations. The problem we address is the design of a filter, such that for all admissible uncertainties, the resulting error system is asymptotically stable and satisfies a prescribed H_∞ performance level. A sufficient condition is obtained to guarantee the existence of desired H_∞ filters, which can be constructed by solving certain linear matrix inequalities. The effectiveness of the proposed design method is demonstrated by a numerical example.