Observer design for sampled-data systems with unknown inputs and uncertainties based on quasi sliding motion

In this paper, the state and unknown input estimation problem is addressed for a sampled-data system whose dynamics is affected by external signals and uncertainties. Unlike the numerous sliding mode observers for dynamical continuous-time systems which employ a nonlinear switching injection term to force the state errors to converge to zero in finite time, the observer design problem for sampled-data systems is often faced with limitations on the hardware, where the sampling time period cannot be made arbitrarily small. Hence, an approximate implementation of an observer, which is designed for a continuous-time system, is not always suitable in the sampled-data context. By exploiting the quasi-sliding motion concept, we propose an observer which takes into account the sampling time period. A theoretical analysis is provided to formally show the convergence of the observer. In the formulation, estimates of the unknown inputs are also given. Simulation results are shown to illustrate the efficacy of the proposed method.