This monograph is driven by the ambition to thoroughly investigate and advance the field of discrete-time sliding mode design based on difference equations with minima for dynamical systems. The motivation behind this exploration lies in the recognition of limitations inherent in classical and conventional control techniques, prompting a quest for methodologies that can effectively address the evolving demands of modern applications. The overarching objective of this monograph is to introduce innovative approaches capable of enabling timely and precise control, even in the presence of uncertainties and exogenous perturbations. Through the development of sophisticated discrete control strategies designed to ensure finite-time convergence, this research aims to enhance the capabilities and operational efficiency of diverse engineering systems, thereby contributing to the ongoing evolution of control methodologies in response to contemporary challenges.