Discrete-Time Adaptive Super-Twisting Observer With Predefined Arbitrary Convergence Time

This brief proposes an adaptive observer based on the super-twisting algorithm (STA) and its discrete-time realization with a predefined convergence time. In contrast to conventional adaptive STA that tries to adaptively reduces the gain sizes as much as possible in accordance with external disturbances, the proposed adaptive observer increases the gain sizes such that the convergence time is ensured to be within the predefined convergence-time period. The numerical chattering associated with these large gains is suppressed by employing the proposed discrete-time realization based on an implicit Euler discretization method. While keeping the property of predefined convergence time, the observation precision of the proposed discrete-time scheme is consistent with the STA, i.e., standard asymptotical second-order accuracy level. The superiority of the adaptive observer and its realization scheme is demonstrated through a circuit system example.