An linear matrix inequality approach to simultaneous fault detection and control design for LTI systems

In this paper, the problem of simultaneous fault detection and control(SFDC) for linear Time Invariant(LTI) systems in continuous-time case is considered, and a new design method of SFDC problem is realized based on linear matrix inequality( LMI). The SFDC problem is formulated as a mixed H₂/H_∞ optimization problem and a state observer is used to reconstruct the faults. By virtue of the Bounded Real Lemma and Shur Complement, a single unit called detector/controller(D/C) is obtained based on LMIs to stabilize the systems and detect the faults. To optimize the performances of the close-loop systems, a D-stable analysis for the D/C is also presented based on LMIs, therefore we can place the pole of the close-loop systems to an appointed region. The result of simulation indicats that the SFDC can stabilize the linear systems with fault happened and the detection can identify the fault clearly.