Input-to-error stable observer for nonlinear sampled-data systems with application to one-sided Lipschitz systems

In this paper the design of sampled-data state observers for nonlinear plants is investigated under the effect of system and measurement disturbance signals. We establish general design principles using the standard approaches of (i) direct discrete-time design via approximation and (ii) discretization of a continuous-time observer (emulation). By interpreting the disturbances as exogenous inputs affecting the error dynamics, sufficient conditions are derived which ensure the input-to-state stability (ISS) of the observer error system in a semiglobal practical sense for the unknown exact discrete-time model. Next, we focus on systems whose vector fields are one-sided Lipschitz to develop constructive design techniques via linear matrix inequalities (LMIs). Numerical simulations of an academic example and a chaotic attractor corroborate the effectiveness of the proposed sampled-data estimators.