Reliable H∞ filter design for a class of continuous-time nonlinear systems with time-varying delay

Abstract—This paper is concerned with the reliable H∞ filtering problem against sensor failures for a class of continuoustime systems with simultaneous sector-bounded nonlinearities and varying time delay. The resulting design is such that the filtering error system is asymptotically stable and meets the prescribed H∞ norm constraint in the nominal case as well as in the sensor failure case. A sufficient condition, which depend not only on the upper and lower bound of delay but also on the upper bound of delay derivative, for the existence of such a filter is obtained by using appropriate Lyapunov functional and linear matrix inequality (LMI) technique. What’s worth mentioning is that the information about the upper bound of delay derivative is taken into consideration even if this upper bound is not smaller than 1. A numerical example is provided to demonstrate the effectiveness of the proposed designs.