 The nominal linear model of the plant is

formula_1

The plant subject to a fault (indicated by a red arrow in the figure) is modelled in general by

formula_2

where the subscript formula_3 indicates that the system is faulty.This approach models multiplicative faults by modified system matrices.Specifically, actuator faults are represented by the new input matrix formula_4, sensor faults are represented by the output map formula_5, and internal plant faults are represented by the system matrix formula_6.