Discrete-time non-linear state observer based on a super twisting-like algorithm

The properties of robustness and finite-time convergence provided by sliding mode (SM) theory have motivated several researches to deal with the problems of control and state estimation. In the SM theory, the super-twisting algorithm (STA), a second-order SM scheme, has demonstrated remarkable characteristics when it is implemented as a controller, observer or robust signal differentiator although the presence of noise and parametric uncertainties. However, the design of this algorithm was originally developed for continuous-time systems. The growth of microcomputers technology has attracted the attention of researchers inside the SM discrete-time domain. Recently, discretisations schemes for the STA were studied using majorant curves. In this study, the stability analysis in terms of Lyapunov theory is proposed to study a discrete-time super twisting-like algorithm (DSTA) for non-linear discrete-time systems. The objective is to preserve the STA characteristics of robustness in a quasi-sliding mode regime that was proved in terms of practical Lyapunov stability. An adequate combination of gains obtained by the same Lyapunov analysis forces the convergence for the DSTA. The problem of state estimation is also analysed for second-order mechanical systems of n degrees of freedom. Simulation results regarding the design of a second-order observer using the DSTA for a simple pendulum and a biped model of seven degrees of freedom are presented.