Deterministic Robust Control for Multiple-Time-Scale Markov Jumping System

This paper gives a deterministic controller design approach for a class of multiple-time-scale Markov jumping linear systems, which admit strong ill-conditioned dynamics. The proposed deterministic controller do not use the jumping mode information, and therefore is very useful in some cases when the jumping information is unavailable. The design procedure reduces to solving a set of bilinear matrix inequalities, which is an NP-hard problem. Therefore, we propose a homotopy algorithm to solve it and obtain the feasible solutions. The numerical examples show the effectiveness of the proposed algorithm.