Robust Fault Detection of Uncertain Time-Delay Markovian Jump Systems with Different System Modes

In this paper, a robust fault detection filter (RFDF)design scheme is presented for uncertain nonlinear Markovian jump systems with mixed delays. By using a observer-based fault detection filter as residual generator, the RFDF design is formulated as an H (a)-filtering problem. Particularly, two different Markov processes are considered for modeling the randomness of system matrix and the state delay; meanwhile, the corresponding two kinds of transition rate matrices are assumed to be incompletely accessible, that is, the one with partially unknown entries and the other with polytopic uncertainties. By using a new convex polyhedron technique, some new sufficient conditions are established in terms of delay-dependent linear matrix inequalities (LMIs) to synthesize the residual generation scheme. Finally, a numerical example is given to illustrate the effectiveness of the proposed techniques.