具有分布时滞线性系统的滑模控制与仿真

摘要

研究时滞控制系统稳定性优化问题,针对一类含有分布时滞和离散时滞的线性系统,对于解决延时问题,提高控制系统的稳定性能,有重要的理论意义和实际应用价值.根据分布时滞的特殊形式特点,构造了Lyapunov泛函,利用稳定性理论、矩阵不等式分析技巧及积分不等式技术,采用线性矩阵不等式形式的结论.选取了滑模面,构造了滑模控制器,使得系统满足滑模到达条件.可通过构造适当的Lyapunov泛函,利用虚拟反馈控制,采用状态反馈的极点配置方法,给出了闭环系统渐近稳定的充分条件.方法设计了时滞独立的滑模面,并简化了滑模控制器的设计.进行仿真,结果说明了滑模控制能确保时滞系统的稳定性,并验证了方法的有效性.%Based on a class of linear systems with distributed delays and discrete delays, It is of important theory and practical applications to study the sliding mode control of time-delay systems in resolving the retard problems and improving the stability performance of control systems. According to distributed delays, the Lyapunov - Krasovskii functional is constructed . By means of stability theory, analysis method of matrix inequality and integral inequality technique, the conclusion is given in terms of linear matrix inequality. Firstly, the sliding mode surface is choosed. Secondly, the sliding mode controller is constructed to satisfy the sliding mode reaching conditions. Finally, the suff-ient conditions of closed-loop systems' asymptotical stability is given by constructing the appropriate Lyapunov func-tionals, in terms of virtual feedback control method and combinating pole assignment of state feedback. Delay-independent sliding mode is given and sliding mode controller is simplefied by the method. The numerical example and simulation are given to illustrate that the sliding mode control can quarantee the stability of time-delay systems, and verify the validity of the method.