非匹配不确定奇异系统变结构控制设计

Design of Variable Structure Control for Mismatched Uncertain Singular Systems

研究一类系统状态矩阵含非匹配不确定项的线性奇异系统的变结构控制设计问题.建立了能控规范受限等价分解形式.基于分解形式,利用线性矩阵不等式方法设计了切换面,并给出了满足系统状态到达切换面条件的变结构控制律.仿真示例表明,该设计方法不仅能保证系统状态轨迹实现滑模运动,而且保证系统的滑模运动正则、无脉冲且渐近稳定.

The design problem of variable structure control for a class of linear singular system with unmatched uncertainties in the state matrix was studied. The equivalent restrict decomposition form was established for the singular system with mismatched uncertainties. On the basis of this form, the switching surface was designed using the linear matrix inequality （LMI） method, and a variable structure control law, which ensures the system state to reach the switching surface, was presented. A simulation example shows that the design method guaranteed not only the sliding mode of the system state trajectory to be realized, but also the sliding mode to be regular, impulse-free, and asymptotically stable.