Robust fault detection filter design for a class of discrete‐time conic‐type non‐linear Markov jump systems with jump fault signals
Xuefei Dong, Shuping He, Vladimir Stojanović
Abstract
This study investigates the robust fault detection filter design problem for a class of discrete‐time conic‐type non‐linear Markov jump systems with jump fault signals. The conic‐type non‐linearities satisfy a restrictive condition that lies in an n ‐dimensional hyper‐sphere with an uncertain centre. A crucial idea is to formulate the robust fault detection filter design problem of non‐linear Markov jump systems as filtering problem. The authors aim to design a fault detection filter such that the augmented Markov jump systems with conic‐type non‐linearities are stochastically stable and satisfy the given performance against the external disturbances. By means of the appropriate mode‐dependent Lyapunov functional method, sufficient conditions for the existence of the designed fault detection filter are presented in terms of linear matrix inequalities. Finally, a practical circuit model example is employed to demonstrate the availability of the main results.