A numerically reliable approach for the synthesis of periodic FDI filters

We propose an integrated numerically reliable computational approach to solve fault detection and isolation (FDI) problems for periodic systems. For this purpose, a bank of periodic fault detection filters providing a structured residual set is designed using a new least order synthesis technique of periodic fault detection filters. The synthesis procedure relies on a recently developed numerically stable algorithm to compute least order annihilators of periodic systems. This approach is extended with two additional steps for the synthesis of least order filters by using periodic dynamic cover techniques and periodic stable coprime factorizations to achieve a desired dynamics of the filters. The proposed integrated synthesis algorithm has strongly coupled computational steps, where the available structural information at the end of each step is fully exploited in the subsequent computations. All computations are done directly on the original problem data, without explicitly building time-invariant lifted system representations.