Optimal robust fault detection

This dissertation gives complete, analytic, and optimal solutions to several robust fault detection problems for both continuous and discrete linear systems that have been considered in the research community in the last twenty years. It is shown that several well-recognized robust fault detection problems, such as H−/H∞, H2/H∞ and H∞/H∞ problems, have a very simple optimal solution in an observer form by solving a standard algebraic Riccati equation. The optimal solutions to some other robust fault detection problems, such as H−/H2 and H2/H2 problems are also given. In addition, it is shown that some wellstudied and seeming sensible optimization criteria for fault detection filter design could lead to (optimal but) useless fault detection filter designs.

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