Design of mixed Luenberger and sliding continuous mode observer using sampled output information

Most of state estimators 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 real applications or even in real systems, one must implement a sampled based observer. This means that output is obtained with an Analogical/Digital Converter and using the sampling-holding device. Using a zero order hold, one can reconstruct the sampled signal until the next measure. In this way, the output information is continuous within the next sampling period. In this paper, a sampled output based second order sliding mode and Luenberger-like observer (SOSML) is developed. A new class of Lyapunov functions is used to prove stability. This so-called strong Lyapunov function was used to demonstrate practical stability leading to define a convergence zone depending on the sampling period. So, this paper introduces the observer design and analyzes the sampling effect on the estimation quality. The result was tested for a simple pendulum system. The efficiency of the suggested SOSML is compared with the a similar sampled version of the so called super-twisting algorithm. The observer performance was evaluated for several sampled times.