Fault detection of switched systems with repeated scalar non-linearities

This study is concerned with the generalised ℋ₂ fault detection problem for a class of discrete-time switched systems with repeated scalar non-linearities. To reduce the overdesign of the quadratic framework, this study proposes a switching-sequence-dependent Lyapunov function approach to the fault detection filter design procedure. Sufficient conditions are obtained for the existence of admissible generalised ℋ₂ fault detection filter. Since these conditions involve matrix equalities, the cone complementarity linearisation procedure is employed to cast the non-convex feasibility problem into a sequential minimisation problem subject to linear matrix inequalities, which can be readily solved by using the standard numerical software. If these conditions are feasible, a desired fault detection filter can be easily constructed. Finally, a numerical example is given to illustrate the effectiveness of the proposed theory.