Adaptive fault diagnosis for a class of linear discrete-time systems via ħλ-order analysis

In this paper, for a class of discrete-time linear time-varying systems, a method for fault detection and diagnosis (FDD) based on adaptive estimation is investigated, and its theoretical properties in detecting faults are established rigorously via the so-called ħ_λ-order analysis. The system model considered is fundamental in term that the majority of practical nonlinear systems can be approximated by linear time-varying systems and the fault model used in this contribution represents the popular nature that usually only limited different kinds of faults with known effects may happen simultaneously with additive effects. The known effect of each fault type is abstracted by a function with respect to time, control inputs and states, and hence the fault detection problem is equivalently converted to a problem of parameter estimation. With the novel approach of ħ_λ order analysis introduced in a companion paper, we are able to identify the conditions to guarantee the convergence or boundedness of parameter estimation errors, in different cases of noise disturbance such as zero noise, bounded noise and diminishing noise.