This paper addresses the mixed H_/H∞ fault detection observer design issue for a class of linear parameter varying (LPV) system. Based on the quadratic H∞ performance , as well as the corresponding quadratic H_ index performance for measuring the worst-case fault sensitivity of the underlying LPV system, the existence conditions of such an observer are given in terms of linear matrix inequalities (LMIs). An algorithm is given to achieve the solutions. An example is studied to demonstrate the effectiveness of the proposed algorithms.© (2011) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.