Design of a functional adaptive observer for bilinear delayed systems

A Functional Adaptive Observer (FAO) for a bilinear system with multiple discrete delays, is proposed in this paper. This observer allow the simultaneous estimation of the states and the unknown parameter. Necessary and sufficient conditions of unbiasedness of the functional observer are given. Stability conditions, which depend on system’s delays, are given in terms of Linear Matrix Inequalities (LMIs) by using a polytopic LPV approach.