Delta-Operator-Based Reaching Laws for Sliding Mode Control Design

Most of the continuous-time algorithms are implemented in the discrete domain. Therefore, it is of utmost importance to have a smooth transition between discrete and continuous time models for enhancing numerical conditioning. Delta-operator is known to provide such flexibility where a delta-operator based dynamic model converges to its continuous counterpart as the sampling time converges to zero. In this brief, delta-operator based novel reaching laws are established. Most importantly, the quasi sliding mode band (QSMB) is calculated via suitable stability analysis in the delta-operator framework. It is shown that when the sampling time converges to zero, the delta-operator based stability analysis provides a similar conclusion to that of continuous-domain analysis. Finally, the theoretical findings are corroborated by some simulation results.