Reliable guaranteed variance filtering against sensor failures

This paper presents a solution to a reliable filtering problem with error variance specifications for both continuous- and discrete-time systems. The filtering error variance in the sensor failure cases is guaranteed to be less than a given upper bound while the performance in the nominal case is optimized. A convergent iterative algorithm based on linear matrix inequality (LMI) is given to obtain the solution. The algorithm solves the problem without introducing additional conservativeness, and it is shown to get better performance and be less conservative compared with traditional LMI approaches. A numerical example is given to show the advantages of our approach over existing techniques.