有界扰动饱和不确定切换系统鲁棒控制器设计

Robust controller design in relation to bounded disturbance saturation uncertainty switching systems

为了避免具有"饱和输入"和"持续有界干扰"的控制系统对性能指标的负面影响,研究了一类有界扰动饱和多胞不确定性切换系统在分段Lyapunov函数切换方式下的稳定鲁棒性.在给定的切换函数作用下,根据分段Lyapunov函数和几个相关引理,推导出使饱和切换系统具有稳定鲁棒性的若干个矩阵不等式约束条件.通过求解矩阵不等式约束条件下的稳定吸引域最优解,设计出使系统达到局部指数收敛的状态反馈控制器,并给出了系统最大吸引域.在持续的扰动条件下,仿真结果表明,该设计方法具有较强的稳定鲁棒性.

In order to avoid negative effects of the control system with ＂ saturation input＂ and ＂ limited persistent disturbance＂ on the system performance, the robust stabilization of a class of bounded disturbance saturation polyto- pic uncertainty switching systems was investigated under the switching mode of a segmented Lyapunov function. Un- der the assumed switched function constraint, according to the segmented Lyapunov function and relative lemmas, a few linear matrix inequality constraints were deduced, ensuring robust stability performance of switching systems with an actuator saturator and limited persistent disturbance. The optimal solution of the stability domain of attrac- tion was obtained through solving the linear matrix inequality constraints. The goal was to design a state feedback controller which makes control systems arrive at locally exponential convergence, setting the domain of attraction to be as large as possible. Under the action of persistent disturbance, the simulation result shows that the proposed de- sign approach has better robust stabilization.