An LMI approach to H_- index and mixed H_- / H_∞ fault detection observer design

Using the newly developed worst-case fault sensitivity measure, the H_- index, and the well-known worst-case robustness measure, the H_∞ norm, this paper addresses the problem of H_- index fault detection observer design and multiobjective H_- / H_∞ fault detection observer design problems. Necessary and sufficient conditions for the existence of such a fault detection observer are given in terms of matrix inequalities. Both infinite frequency range case [0, ∞) and finite frequency range case [0, over(ω, -)) are considered. Iterative linear matrix inequality (ILMI) algorithms are given to obtain the solutions. The effectiveness of the proposed approaches is shown by numerical examples.