针对一类具有时变时滞和Markov跳变参数的不确定系统, 研究基于滑模超平面的变结构控制算法. 该算法通过坐标变换将系统描述成简约型, 在考虑时变时滞和不确性的前提下, 基于线性矩阵不等式(LMIs)方法给出了滑模平面的设计方法, 推导出了随机稳定滑模面存在的充分条件, 同时利用指数趋近律构造了整个系统的滑模变结构控制算法, 并证明了该算法能够确保系统的运动轨迹在有限时间内到达并一直保持在滑模面上.最后通过数值仿真算例验证了设计方法的正确性和有效性.

For a class of uncertain systems with time-varying delay and markov jumping parameters, a variable structure control algorithm is proposed based on liding-mode surface. By using a nonsingular transform of the system, a sufficient condition for the existence of stochastic stable sliding surfaces depending on the time-varying delay and uncertainties bounds is established in terms of linear matrix inequalities (LMIs). On the basis of this existence condition, a sliding-mode control algorithm is designed via exponential approach law, which is proved to guarantee that the system trajectory reaches the sliding surface in a finite time interval and keeps up here thereafter. Finally, an illustrative example demonstrates the correctness and feasibility of the proposed approach.