State Space Solution to the H<sub>-</sub>/H<sub>∞</sub> Fault Detection Problem

Abstract

In this paper we give a state space solution to the H_-/H_∞ fault detection (FD) problem for linear time invariant dynamic systems. An H_-/H_∞ FD filter minimizes the sensitivity of the residual signal to disturbances while maintaining a minimum level of sensitivity to faults. We provide a state space realization of the optimal filter in an observer form via the solution of Linear Matrix Inequalities (LMIs). A numerical example is given to illustrate the algorithm.