Differential Linear Matrix Inequalities in Optimal and Robust Sampled-Data Filtering

This paper tackles the design of a robust filter for sampled-data linear time-invariant systems subject to parameter uncertainties. After the optimal solution is obtained, the two major classes of parameter uncertainty are considered, namely, convex bounded and norm bounded. For each of them, the filter associated to the minimum H2 guaranteed performance is determined. The design conditions are expressed through differential linear matrix inequalities (DLMIs), a mathematical device well adapted to cope with sampled-data systems because it naturally avoids matrix exponential and similar mappings. In this framework, the optimal nominal filter is determined, and it is shown that it exhibits a time-invariant observer-based structure. Illustrative examples are presented and discussed in order to put in clear evidence the theoretical results.