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

Using the newly developed worst-case fault sensitivity measure, the H-H- index, and the well-known worst-case robustness measure, the H∞H∞ norm, this paper addresses the problem of H-H- index fault detection observer design and multiobjective H-/H∞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,∞)[0,∞) and finite frequency range case [0,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.