Sampled-data observer for one-sided Lipschitz systems: Single-rate and multirate cases

The problem of sampled-data observer design is addressed for the so-called nonlinear systems with one sided Lipschitz nonlinearity in presence of disturbance inputs. We first develop a single-rate observer using a refined Euler model formulated via tractable linear matrix inequalities (LMIs). This scheme is shown to be input-to-state stable from exogenous disturbances to the estimation error in a semiglobal practical sense for the unknown exact discrete-time plant model. Then, the proposed observer is modified appropriately to cope with the practical case of multirate sampling by preserving similar stability property. A simulation example justifies the efficiency of both observers for the one-sided Lipschitz systems and demonstrates the superiority of the multirate observer when the input and output signals are sampled at different rates.