Lmi-based Integration of Robust H∞ -control and Rfd for Lti Systems

In this contribution, problems related to the integrated design of observer-based robust H∞ controller and robust fault detection (RFD) system is studied for uncertain LTI systems with both modelling errors and unknown input. We first propose to use an ideal solution, which is in fact an optimization solution of fault detection filter achieved on the assumption of the system model is perfectly known (i.e. without modelling errors), as the reference model of robust fault detection filter design for uncertain systems. The integrated design can then be formulated as a two-objective H∞−optimization problem which is solved using LMI techniques. The basic idea behind our study is that the robust H∞ controller share a common observer with the fault detection filter; by introducing a reference residual model, the feedback controller and robust fault detection filter can be designed together via solving a two-objective H∞−optimization problem; finally an LMI approach to integrated design is developed. An example is also presented to illustrate the proposed approach.