On Optimal Fault Detection for Discrete-time Markovian Jump Linear Systems

This paper deals with the problem of fault detection for discrete-time Markovian jump linear systems (MJLS). Using an observer-based fault detection filter (FDF) as a residual generator, the design of the FDF is formulated as an optimization problem for maximizing stochastic H−/H∞ or H∞/H∞ performance index. With the aid of an operator optimization method, it is shown that a unified optimal solution can be derived by solving a coupled Riccati equation. Numerical examples are given to show the effectiveness of the proposed method.