Discrete-time chattering free exponentially stabilizing sliding mode scalar control via Lyapunov’s method

Linear time-invariant discrete-time plant, with no restrictions on the form of the state equation and with scalar control, is considered. The exponentially stabilizing state feedback control algorithm is developed by Lyapunov’s second method leading to the variable structure system with chattering free sliding modes. Essentially, the control algorithm drives the system from an arbitrary initial state to a prescribed so-called sliding subspace S, in finite time and with prescribed velocity estimate. Inside the sliding subspace S, the system is switched to the sliding mode regime and stays in it forever. The proposed algorithm is tested on the real system in practice, direct current (DC) servo motor, and simulation and experimental results are given. Also, it is compared with another already known algorithm from literature.