Robust fault detection of Markovian jump systems with different system modes

This paper deals with the robust fault detection filter (RFDF) design problems for uncertain nonlinear Markovian jump systems with unknown input. By using a observer-based fault detection filter as residual generator, the RFDF design is formulated as an H∞H∞-filtering problem. Particularly, two different Markov processes are considered for modeling the randomness of system matrix and the state delay. With the aid of the weighting matrix function, the design objective is to find an optimal RFDF, which results in a minimal difference between the reference model and the RFDF to be designed. By using a new convex polyhedron technique and two mode-dependent Lyapunov functional, 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.