基于LMI的混合系统的稳定性和鲁棒镇定研究

混合系统的稳定性分析，乃至镇定方法是混合系统研究的重要内容。线性多模态切换系统是一类重要的混合系统。针对线性多模态系统提出了一种基于线性矩阵不等式技术进行稳定性分析和鲁棒镇定的方法，通过求解一组线性不等式得出稳定性的判定条件，设计出的一组状态反馈控制律对系统的模态切换乃至有界模型不确定有鲁棒性。推导了控制律设计所对应的线性矩阵不等式组，并证明了其中的一致性关系，探讨了求解方法，应用实施也显示出该方

On the Stability and Robust Stabilization of Hybrid System via LMI

Hybrid system is a system combined with time evolving and event driven mechanism and is becoming more and more important these years. Stability and stabilization issue of hybrid system are discussed in the paper, where some sufficient conditions for stability and stabilization in terms of several sets of linear matrix inequalities are given to determine if a linear switched system is stable, stabilized robustly or not. Several items in terms of linear matrix inequalities related to mode area information and switched conditions are explored to decrease the conservatives of solutions, while as to issue of robust stabilization, several other items associated with uncertainties can be added to derive the control law which can be robust to uncertainties. Illustrative examples show the effectiveness of proposed methods.