不满足匹配条件的非确定性系统的鲁棒滑模控制

摘要

In this paper, the SMC approach is applied to the system in order to establish robust stability against uncertainties both in the system matrix and input matrix. The method of switching surface designing and the control law are given. Sufficient conditions under which the sliding mode system is quadratically stable are also deduced. The relative algebraic Riccati equation and linear matrix inequality are quite simple, thus can be solved without much difficulty. Simulation results confirm the validity of the scheme.%针对一类非确定性时变系统实施滑模控制，该系统在状态矩阵和控制输入矩阵中都包含不满足匹配条件的不确定项.给出了能使系统鲁棒镇定的切换面设计方法和相应的控制律的形式.同时，也给出了系统渐近稳定的充分条件.设计过程中的代数黎卡提方程和线性矩阵不等式形式简单，易于求解.仿真结果证明了理论的正确性.