New Approach to Mixed H2/H∞ Filtering for Polytopic Continuous-time Systems

This paper discusses the problem of mixed H₂/H_∞ filtering for continuous-time systems. In the case where the state-space matrices of the system depend affinely on the uncertain parameters, it is known that recently developed extended or dilated linear matrix inequalities (LMIs) are effective to assess the robust performance in a less conservative fashion. In this paper, the filter is designed by using different Lyapunov matrices to the mixed performances. These ideas are realized by introducing additional slack variables to the well-established performance conditions and by employing new bounding techniques, which results in a much less conservative filter design method. A numerical example is presented to illustrate the effectiveness and advantage of the developed filter design method