凸多面体不确定系统的符号稳定性分析

Sign stability analysis of polytopic uncertain systems

中文关键词  符号稳定  控制综合  不确定系统  姿态控制

英文关键词  sign stability  control synthesis  uncertain systems  attitude control

中文摘要

      针对一类凸多面体描述的连续线性不确定系统研究其符号稳定性条件, 从而从符号稳定的角度探索一种新的不确定系统鲁棒控制器设计方法. 在矩阵符号稳定定义和必要条件的基础上, 给出了矩阵集合符号稳定的定义和完整同源稳定符号型集合的概念, 得到了凸多面体不确定系统符号稳定的充分必要条件. 进一步分析了符号稳定凸多面体不确定系统的特征根分布与主对角线元素的关系, 提出了基于符号稳定的不确定系统状态反馈镇定控制综合方法. 相比于基于Lyapunov稳定性理论的不确定系统鲁棒控制方法, 本文所提方法避免了求解线性矩阵不等式, 并且更符合工程设计的习惯. 通过一类三轴稳定卫星姿态控制问题的算例和仿真验证了所提方法的有效性.

英文摘要

      Considering a class of polytopic continuous linear uncertain systems, the sign stability condition is researched in order to explore a new robust control design approach for uncertain systems. On the basis of the definition and necessary conditions for the sign stability of matrix, the sign stability of matrix set is defined, and the concept of complete isogenous sign stable set is presented. Then the necessary and sufficient condition of sign stability for the polytopic uncertain systems is acquired. The relationship between the eigenroots and principal diagonal elements of sign stable polytopic uncertain systems is analyzed, and the state feedback stabilization control synthesis approach based on sign stability is provided. Compared with the robust control technique based on Lyapunov function method, the achieved approach avoids the resolution of the linear matrix inequalities and accords with the engineering practice. A computation and simulation example of satellite attitude control problem is given to validate the proposed method.