Robust Control for Singularly Perturbed Markov Jumping Linear Systems

In this paper, a robust controller design approach for singularly perturbed Markov jumping systems, which admit strong ill-conditioned dynamics. The proposed robust controller do not use the jumping mode information, and therefore is very useful in some cases when the jumping information is unavailable. Other than our previous results, the design procedure reduces to solving a set of linear matrix inequalities, but not bilinear matrix inequalities. The numerical examples show the effectiveness of the proposed algorithm.