摘要
综合运用比较原理和LMI方法.首先通过构造一比较系统,将原组合系统的稳定性问题转化为讨论维数低的比较系统的稳定性问题,并利用M矩阵特性导出了比较系统稳定的一个充分条件;为了求取输出反馈增益,建立了等价的稳定条件的QLMI表示形式.通过建立QMI中一矩阵变量的递推关系,将QMI问题转换为一替代过程的LMI求解问题,进而通过求解这一LMI问题来获取可镇定的非线性组合系统输出反馈增益阵.这一方法的特点是使大系统的稳定控制器设计的复杂度保持在子系统一级的水平上,文末给出的数值实例说明了算法在实际工程应用中是有效的.
A comparing model is introduced to transfer the problem of output feedback for stabilizing the Lurie composite nonlinear systems into output feedback stabilizing the comparison systems of lower dimensions, by employing differential and Lyapunov stability theory integrally. A stability condition is developed in form of M matrix, the corresponding LMI expression is founded, which leads to an iterative approach to obtain the output feedback gain. An algorithm to obtain the output-feedback gain matrix is developed here based on the LMI technique. The key technique of developing iterative law of the matrix variable existing in QMI is discussed also. The character of the results proposed here is decreasing complexity. Finally, a numerical example is given to illustrate our results and its application.
出处
《湘潭大学自然科学学报》
CAS
CSCD
北大核心
2008年第1期8-13,共6页
Natural Science Journal of Xiangtan University
基金
湖南省科技计划项目(05GK2003)资助
