Steady-state analysis of discrete-time nonsingular terminal sliding mode control systems based on Euler method

In this article, the steady-state behaviors of discrete-time nonsingular terminal sliding mode (NTSM) control systems are investigated for the explicit and implicit Euler integration schemes. It is demonstrated that implicit Euler method can guarantee the global convergence of both system states and sliding variable for discrete-time NTSM control systems, whereas explicit Euler approximation does not. For explicit discrete-time NTSM, the range of quasi sliding mode band is deduced on the basis of the reachability condition of discrete SM, showing that discretized NTSM can achieve higher control accuracy than the discrete-time linear sliding mode. By analyzing the distribution features of steady-state points, the upper bound for steady states is obtained to estimate chattering amplitude, which establishes the influence relationship of sampling time, switching gain and movement characteristics on the bound of steady states. Simulations are presented to validate the theoretical results.