Lyapunov stability analysis of discrete-time robust adaptive super-twisting sliding mode controller

This paper presents a discrete-time Robust Adaptive Super-Twisting Sliding Mode controller and its stability analysis by means of Lyapunov stability theory. The control law is composed by two different control structures: a Robust Model Reference Adaptive Controller (RMRAC) and an Adaptive Super-Twisting Sliding Mode (STSM) Controller. The main advantage of the control structure is its robust performance and high adaptability in face of unmodelled dynamics, presenting a fast reference tracking without chattering, since it uses a second-order Sliding Mode action into adaptive control structure. The stability and robustness analysis of the control structure are presented in discrete time, considering the overall plant, that is, in presence of matched and unmatched dynamics. In addition, the control structure performance is corroborated with simulation results, considering a non-minimum phase unstable plant. Moreover, the presented results are compared with an adaptive first-order SM control-based RMRAC, which can be clearly seen that proposed controller has better performance, mainly by means of chattering mitigation.