Fault-tolerant control of Markovian jump systems via a partially mode-available but unmatched controller

In this paper, a kind of fault-tolerant controller is proposed to study the stabilization problem of continuous-time Markovian jump systems, whose operation modes are not only partially-available but also unmatched. Here, the above general properties of a controller are modeled to be a polytopic controller with uncertainties. Based on the proposed model, concise conditions for the existence of such a controller are proposed with LMI forms, which are extended to consider observer design problem too. Compared with the traditional methods, not only is the designed controller more general but also the established results are fault free and could be solved directly. Finally, numerical examples are used to demonstrate the effectiveness of the proposed methods.