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

• Published in: IET control theory & applications Vol. 14; no. 14; pp. 1912 - 1919
• Main Authors: Dong, Xuefei, He, Shuping, Stojanovic, Vladimir
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 24.09.2020
• Subjects: augmented Markov jump systems; conic‐type nonlinearities; control system synthesis; designed fault detection filter; discrete‐time conic‐type nonlinear Markov jump systems; fault diagnosis; filtering theory; jump fault signals; linear matrix inequalities; Lyapunov methods; Markov processes; nonlinear control systems; Research Article; robust control; robust fault detection filter design problem; stochastic systems; time‐varying systems; uncertain systems; time-varying systems; fault diagnosis; discrete-time conic-type nonlinear Markov jump systems; uncertain systems; filtering theory; robust fault detection filter design problem; control system synthesis; augmented Markov jump systems; conic-type nonlinearities; linear matrix inequalities; nonlinear control systems; designed fault detection filter; stochastic systems; Markov processes; jump fault signals; robust control; Lyapunov methods
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2019.1316

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 $H_\infty $H∞ 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 $H_\infty $H∞ 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.