Insensitive reliable H∞ filtering against sensor failures

This paper investigates the problem of insensitive reliable H∞ filter designs for linear time-invariant continuous-time systems against sensor faults and filter coefficient variations. The considered faults are more general state-dependent bias/stuck-sensor faults. Based on mode-dependent Lyapunov functions, a novel insensitive reliable H∞ filter is constructed in the framework of linear matrix inequalities (LMIs) technique to guarantee the stability and optimize the expanded H∞ performance index of the filtering error system. Moreover, some filter parameter functions are introduced to compensate the effect of sensor faults, as well as to eliminate the filter coefficient variations. The relationship among performance degradation of systems, sensor fault and coefficient variation compensations is clearly demonstrated by LMIs. A numerical example is carried out to illustrate the effectiveness and superiority of the proposed design method.