Evaluation function based fault detection for linear discrete-time stochastic systems

This paper deals with the problem of fault detection for a class of linear discrete-time varying stochastic systems in the framework of minimizing a quadratic form. Instead of residual generation, we formulate the problem of fault detection as to find a minimum of quadratic form over unknown initial state. A sufficient and necessary condition to the minimum is then given in terms of Riccati recursion and the obtained solution delivers an efficient evaluation function of fault detection. Furthermore, strategies of statistic testing are also discussed and a numerical example is given to illustrate the proposed method.