This paper proposes a new robust Discrete-Time Sliding Mode Control (dt-smc) scheme for linear discrete-time delay system. The delays, affecting the state and the input, are assumed to be known, time-varying and bounded. The considered system is also subject to time-varying Unknown But norm-Bounded (ubb) unmatched uncertainties, that act on the state and the delayed state vectors. The designed controller is based on a novel sliding surface. Using a new Lyapunov functional candidate and by introducing slack variables, a less conservative delay-dependent sufficient condition ensuring the asymptotic stability of the closed loop system is derived in terms of Linear Matrix Inequalities (lmis). With respect to that condition a new dt-smc law is synthesized. The proposed control algorithm is applied to an Autonomous Underwater Vehicle (auv). The simulation results demonstrate the effectiveness of the proposed controller.

本文针对线性离散时间延迟系统提出了一种新的鲁棒离散时间滑模控制（dt-smc）方案。影响状态和输入的延迟被假定为已知的、随时间变化的和有界的。所考虑的系统还受到时变未知但范数有界 ( ubb ) 不匹配的不确定性的影响，这些不确定性作用于状态和延迟状态向量。设计的控制器基于一种新颖的滑动面。使用新的李雅普诺夫函数候选并通过引入松弛变量，根据线性矩阵不等式 ( lmi s)推导出一个不太保守的延迟相关充分条件，以确保闭环系统的渐近稳定性。关于这种情况，一个新的dt-smc法是综合的。所提出的控制算法应用于自主水下航行器 ( auv )。仿真结果证明了所提出的控制器的有效性。