Design of variable gain super-twisting observer for nonlinear systems with sampled output

Most of state observers implemented in real systems are not able to measure the information continuously. The sliding observers are not an exception. Nevertheless, when state observers are used in numerical applications or even in real systems, one must implement a sampled based observer. This means that the output was obtained by means of a Analogical/Digital Converter. Using a zero order hold we can maintain the data until the next measure. In this form the output implemented in the algorithm is continuous. In this paper, a novel variable-gain super-twisting observer is proposed based on Lyapunov theory. That is, the correction terms varies during the time. This variable gain depends on the error trajectories and known functions that are upper bounds for the disturbances that affect the system. The observer ensures finite time convergence into a boundary layer depending of the sampled period. This structure is applied in a simple pendulum model using several sample periods of time.