不确定广义系统多约束指标的相容性

Consistency of multiple constraint indices for uncertain descriptor systems

针对一类线性不确定广义系统,研究了容许性、H∞指标和状态方差相容条件下的输出反馈控制器的设计问题.首先建立了一个使闭环广义系统满足容许性和给定H∞指标的充要条件;然后利用quasi-Newton方法,将非线性矩阵不等式的可行解问题转化为求解最大特征值的最小问题,在广义系统容许的条件下,对具有指定∞指标及相容状态方差约束的控制问题给出了满意控制设计方法,同时给出了方差约束指标的取值范围;最后,仿真结果表明了所提出方法的有效性,且更能保证系统的动态性能.

The consistency of constraint indices of admissibility,H∞ and state variance is investigated for a class of uncertain descriptor systems with the output feedback control.Firstly,a necessary and sufficient condition is presented for the closed-loop descriptor system with admissibility and H∞ constraints are given.Then,by using quasi-Newton approach,the solvability of nonlinear matrix inequality is transformed into the minimization problem of maximum eigenvalue.Satisfactory control design methods are provided for the output feedback control with constraints of admissibility,∞ and consistency state-variance,and a range is presented for the state-variance which is consistent with the given ∞.Finally,a numerical example illustrates that the proposed method is effective and can guarantee the dynamic performance of the system.