不确定广义双线性系统的鲁棒无源控制

摘要

The robust passive control problem for a class of uncertain singular bilinear systems is investigated. By means of generalized Lyapunov function and generalized Riccati inequality and linear matrix inequality, a sufficient condition is derived such that a prescribed uncertain singular bilinear system is passive and its zero solution is asymptotically stable. By making use of the method of norm bounded and limited collection, a state feedback control law is designed such that the closed--loop system is passive and its zero solution is asymptotically stable. Finally, an example is given to illustrate the validity of the obtained results.%研究了不确定广义双线性系统的无源控制问题.利用广义李雅普诺夫函数、广义黎卡提代数不等式和线性矩阵不等式,给出了不确定广义双线性系统的零解渐近稳定和无源的充分条件.特别针对广义双线性系统,采取了范数有界和集合限定的方法,设计了状态反馈控制器,使得闭环系统是零解渐近稳定且具有无源性,同时给出了相应的控制器的构造.最后,给出了一个实例说明所得结论的正确性.