Fault Detection for Linear Discrete Time-Varying Systems with Multiplicative Noise: The Finite-Horizon Case

This paper studies the problem of fault detection for linear discrete time-varying systems with multiplicative noise in finite-horizon, where our main object is to provide an optimal fault detection filter (FDF) design scheme such that stochastic sensitivity/robustness ratio for fault diagnosis is maximized in the sense of probability 1. An operator-aided optimization approach and a generalized FDF are proposed such that solutions to the filter design issues are derived in the operator forms. The relationships among the deduced solutions are explicitly revealed via the proposed operator-aided methodology. The parameter matrices of the filter are computed in an analytical way by solving some recursive matrix equations. It is shown that the addressed approaches establish an operator-based framework of optimal FDF design for some categories of linear discrete-time systems. An example is given to illustrate the efficacy of our algorithms.