Summary: In this article, a novel adaptive reaching law is developed to address discrete-time sliding mode control systems with mismatched uncertainties. By using the high-order disturbance compensator, a new reduced-order sliding surface is constructed to avoid redundancy and decrease superfluous computational expense. Then, an adaptive reaching law with adjustable switching gain is designed to guarantee globally fast convergence of sliding variable. Compared with existing similar works, the proposed reaching law has a main advantage that it can obtain arbitrarily small width of quasi sliding mode domain, leading to suppressed chattering. Based on the analysis of the closed-loop system, the upper bound of steady states is established. The whole control scheme is able to counteract mismatched uncertainties and achieve high-precision control at the same time. Finally, a simulated example on bank-to-turn missiles is given to verify this research achievement.
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