Fault detection filter design of delta operator systems with control delays

This paper focuses on the problem of robust fault detection filter design for delta operator formulated systems with control delays. By using state feedback control law, delta operator systems with control delays can be converted to systems with state delays. Then, based on the traditional robust fault detection filter design method, a new filter by replacing the shift operator with the delta operator is discussed for this kind of systems. The sufficient conditions for the existence of the delta operator filters are given with linear matrix inequalities (LMIs) and Lyapunov function technique. With Matlab LMI Control Toolbox to solve the convex optimization problem, the optimal filters for delta operator-based systems with control delays are obtained. A numerical example is provided to show the effectiveness of the proposed design approach.