All H∞ singular and normal filter design for uncertain singular systems

In this short paper, the H_infin filter design for uncertain singular systems is considered. We study to design normal filters and singular filters for the same singular systems. Via using linear matrix inequalities (LMIs), the sufficient conditions are established for the existences of two kinds of filter forms such that two uncertain error systems are admissible and their transfer functions from the disturbance to the filtering error output satisfy a prescribed H_infin-norm bound constraint. By solving LMIs, explicit parameterization expressions of all desired normal filters and singular filters are obtained. Furthermore, all results involve no decomposition the original singular system matrices. It makes that the procedure of filter design is simple and direct. Simultaneously, we still optimize and compare with their H_infin performances for uncertain error systems under two kinds of filter cases. Finally, a numerical example is given to illustrate the effectiveness of the proposed design method and compare with their H_infin performances.