不确定奇异系统的鲁棒控制

Robust control of uncertain singular systems

在参数不确定性F范数有界的情况下,给出了具有此类不确定性的奇异系统广义二次稳定及其可稳的定义.基于定义,构造出严格的线性矩阵不等式(LMI),然后利用矩阵的Schur补性质论证了在线性矩阵不等式的条件下,此类不确定奇异系统(包括闭环系统)是正则、脉冲自由和稳定的.同时给出了具体的状态反馈u(t)=δ-1GTx(t),并通过数值例子验证了此方法的可行性.

The concepts of generalized quadratic stability and generalized quadratic stabilization for uncertain singular systems are given in the case that parametric uncertainty F is norm bounded. With these concepts, some strict linear matrix inequalities （LMI） are developed based on these linear matrix inequalities and the matrix Schur complement. It is proved that uncertain singular, including closedloop, systems are regular, impulse free and stable for all admissible uncertainties. Also a state feedback controller u （ t ） = δ^- 1 G^Tx （t） is formulated, Finally, some examples are provided to demonstrate the applicability of the proposed approaches.