不匹配不确定时滞系统的自适应变结构控制

Adaptive variable structure control for delay systems with mismatched uncertainties

针对一类带有不匹配时变不确定性和时滞的线性系统 ,基于 L yapunov稳定性定理 ,提出了一种新的自适应变结构控制策略 .该控制策略保证了闭环系统滑动阶段的存在性 ,由于不满足通常的匹配条件 ,在设计线性滑模面的系数矩阵时提出了一种新的匹配条件 ,并在此基础上很容易地证明了滑动模态运动相对于不匹配时变不确定性和时滞的完全不变性 ;因而一旦系统运动轨迹到达滑动模态 ,系统将会沿着滑模面作期望特性运动 ,从而确保了系统的全局稳定性 .通过仿真例子说明了该控制策略的可行性和有效性 .

For a class of uncertain time-varying time-delay linear systems which do not satisfy the matching conditions, an adaptive variable structure control strategy is proposed based on Lyapunov stability theorem. The control strategy can guarantee the existence of the closed-loop system's sliding phase. Since the conventional matching conditions are no longer wet, the coefficient matrix of the sliding function can be designed to satisfy a new matching condition. It is shown that the system is invariant on the sliding surface. Once the dynamics of the system come into the sliding mode, the motion should continue on the sliding surface, and under which condition, the global stability of the closed-loop system is guaranteed Analysis of the simulation results of a numerical example showed that this design method is feasible and effective.