不确定离散系统最优保性能控制的改进

Extension of optimal guaranteed cost control for uncertain discrete-time linear systems

针对一类具有范数有界时变参数不确定性的离散时间线性系统 ,通过分析保性能控制与其闭环性能指标之间的关系 ,指出性能指标中的加权矩阵只需要半正定 ,而不要求必须正定 ;并给出了在加权矩阵为半正定的情况下 ,利用线性矩阵不等式 (LMI)实现保性能控制的方法 ;最后通过一个例子说明了本文所提方法的有效性 .该方法大大增加了保性能控制中权值选取的灵活性 ,使输出跟踪等问题都可以方便地通过适当变形转化为该问题的形式来求解 。

For a class of discrete-time linear systems with norm-bounded time-varying parameter uncertainty, the relation between guaranteed cost control and its cost index was analyzed. It was found that the weighting matrices in the cost index can be semi-positive rather than positive. So it presents a new method to realize guaranteed cost control by linear matrix inequalities when the weighting matrices are semi-positive. An example was given. This method enhances the flexibility in selecting weighting matrices greatly and extends the scope applied. Some problems such as output tracking problem can be solved through transformation.