An LMI-based H _-/ H _∞ optimal design approach for fault detection observer

By constructing a linear full-order observer for linear time invariant system, the dynamics of residual generator is acquired which involves unknown inputs represented by disturbances, noise, model uncertainty and faults. The sensitivity fault is described by H _- index, and the robustness of residual to unknown input signal is denoted by H _∞ norm. Therefore the design problem of fault detection observer can be described as an optimization one. After the design of linear matrix inequality-based fault detection observer is studied, the solution of optimal observer gain is given, and the existence condition of its solution is also derived. The designed fault detection observer has high sensitivity to faults and strong robustness to unknown inputs.