二阶离散系统LQ问题加权阵的选择

本文针对单输入条件下二阶定常线性离散系统,讨论了线性二次型(LQ)问题中加权阵的选择问题。证明并给出了当要求闭环系统是渐近稳定时,加权阵与系统开、闭环特征多项式之间以及系统开、闭环极点之间的一组解析关系式。对实例的计算结果表明,利用这组关系,可以很方便地得到加权阵。

Choice of Weighted Matrix of LQ Problem for Second Order Discrete System

The problem of choosing weighted matrix of LQ for second order discrete system in the case of single input is discussed here in the article. Also proved and given are analytic relations between weighted matrix and the multinomial eigenvalue of the System and that between weighted matrix and both open - loop and close - loop systems when close -loop is stable. The result of computation shows that it is very easy to get the weighted matrix by making use of these relations.