Stabilization of Discrete-Time Markovian Jump Systems by a Partially Mode-Unmatched Fault-Tolerant Controller

In this paper, a kind of fault-tolerant controller is proposed to study the stabilization problem of discrete-time Markovian jump systems, whose operation modes are not only partially-available but also unmatched. Here, such general properties of controller are modeled to be a controller having polytopic forms and uncertainties simultaneously. Based on the proposed model, concise conditions for the existence of such a controller are proposed with linear matrix inequality (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.