Robust fault detection filter design for a class of discrete‐time conic‐type non‐linear Markov jump systems with jump fault signals

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.