Variable structure control for mismatched uncertain systems using output variables with finite-time convergence

In this paper, a novel variable structure control (VSC) approach is investigated for a class of mismatched uncertain systems. The VSC approach, which includes output variables only, shows finite-time convergence of the sliding mode, complete invariance to the matched uncertainties, the asymptotic stability property, and is free of the chattering phenomenon. A suitable reduced-order observer (ROO) is constructed to estimate the unmeasured variables. Additionally, a novel finite-time sliding-mode controller (FTSMC), based on the constructed ROO and the output variables, is proposed to stabilize a class of mismatched uncertain systems. To ensure finite-time stability and chattering removal, a discontinuous FTSMC is replaced by a continuous FTSMC utilizing a tanh function. Moreover, a new linear matrix inequality (LMI) condition is derived so that the system in the sliding mode is not only completely invariant to matched uncertainties but also asymptotically stable. Finally, a numerical example is presented, which demonstrates the effectiveness and advantages of this method.