基于LMI的不确定切换系统鲁棒控制

Robust Control for Uncertain Switched Systems Based on LMI

基于线性矩阵不等式(LMI)方法和凸组合技术,研究一类带有非线性扰动的不确定切换系统的鲁棒镇定问题。在每个子系统均不能镇定的情况下,利用单李雅普诺夫函数方法和多李雅普诺夫函数方法,分别得到不确定切换系统可镇定的充分条件。针对参数不确定性的未知、时变、有界特点,设计出鲁棒状态反馈控制器及相应的切换策略。最后,通过计算机仿真验证所设计方法的正确和有效性。

Based on LMI （linear matrix inequality） method and convex combination technique, the problem of robust stabilization for a class of uncertain switched systems with nonlinear disturbance is studied. By using single Lyapunov function technique and multiple Lyapunov function technique, sufficient conditions of robust stabilization for switched systems are obtained respectively under the assumption that each subsystem can＇ t be stabilized. The parameter uncertainties are tlme- varying and unknown but are norm - bounded. Robust state feedback controllers and two classes of switching laws are designed. The simulation results show the validity of the designed methods.