Observer design for linear multi-rate sampled-data systems

This paper addresses observer design for linear systems with multi-rate sampled output measurements. The sensors are assumed to be asynchronous and to have uncertain nonuniform sampling intervals. The contributions of this paper are twofold. Given the maximum allowable sampling period (MASP) for each sensor, the main contribution of the paper is to propose sufficient Krasovskii-based conditions for design of linear observers. The designed observers guarantee exponential convergence of the estimation error to the origin. Most importantly, the sufficient conditions are cast as a set of linear matrix inequalities (LMIs) that can be solved efficiently. As a second contribution, given an observer gain, the problem of finding MASPs that guarantee exponential stability of the estimation error is also formulated as a convex optimization program in terms of LMIs. The theorems are applied to a unicycle path following example.