严格耗散广义系统的鲁棒性分析与控制

Robust strict dissipativeness analysis and control for singular systems

考虑不确定广义系统的鲁棒耗散性分析与控制,其中各不确定参数矩阵具有线性分式形式。针对确定广义系统建立耗散性与正实性之间的等价关系,将不确定广义系统的鲁棒耗散性分析与控制转化为确定广义系统的耗散性分析与控制,利用线性矩阵不等式,给出了不确定广义系统鲁棒严格耗散的充要条件及状态反馈鲁棒严格耗散控制器的设计方法。通过一个数值算例说明所给设计方法的有效性。

The robust dissipative control problem for uncertain singular systems is considered where the uncertainties are expressed in a linear fractional form. Equivalence between dissipativeness and positive realness is established, and necessary and sufficient conditions are derived for singular systems to be strictly dissipative. The dissipative analysis and control of the uncertain singular systems are reduced to those of related systems without uncertainties. By means of linear matrix inequalities（LMIs）, a sufficient and necessary condition that guarantees robust strict dissipativeness of uncertain singular systems is given, the state feedback controller is designed. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.