Lyapunov-stability for the sliding-mode control of a turbocharger subject to state constraints

We consider the robust control design for the boost-pressure control of an exhaust-gas turbocharger of an internal combustion engine. We design a sliding-mode controller using the super-twisting algorithm. In our main contribution we present a thorough stability analysis based on two different Lyapunov functions, one for the reaching phase and one for the sliding-phase. Additionally, we consider state-constraints for each of the control phases and guarantee that the state stays within prior defined bounds.