Observer design with mixed continuous and multirate sampled outputs involving multiple time-varying delays

A high gain observer is proposed for a class of multi-output uniformly observable systems involving external disturbances. Each output may be available with a delay under a mixed form, i.e. continuously in time over some time intervals and only at sampling instants over other ones. Moreover, each output is associated to a sampling partition and a delay without assuming any relation between the considered sampling partitions, nor the output delays. The corner stone of the proposed observer design consists in the consideration of an appropriate observer gain issued from the resolution of a linear Delay Differential Equation (DDE) which accounts for all the sampling partitions as well as the presence of the output delays. It is worth noticing that the proposed observer has the same dimension as the system whenever the output delays are relatively small. The convergence analysis related to the proposed observer is performed thanks to a comprehensive Lyapunov approach under a well-defined condition on the sum of the upper bound of the sampling partition diameters and of the upper bound of the time-varying outputs delays. The performance of the proposed observer and its main properties are highlighted through an example dealing with a flexible joint robot arm.