线性连续重复过程的H_∞模型降阶

H_∞ model reduction for linear differential repetitive processes

研究连续时间线性重复过程的H∞模型降阶问题,目的是设计一个低阶的重复过程来近似原高阶的重复过程,使得误差在H∞性能指标下达到最小.首先给出误差系统沿通道稳定且满足H∞性能指标的充分条件';然后采用投影定理来解决模型降阶问题.得到的条件不完全是线性矩阵不等式的形式,采用锥补线性化算法进行计算求解.仿真实例证实了该设计方法的有效性.

This paper investigates H∞ model reduction problem for linear ditterenttal repetitive processes. attention is focused on the construction of a reduced-order stable along the pass process, such that the H∞ gain of the error process between the original process and reduced-order one is less than a prescribed scalar. A sufficient condition to characterize the bound of H∞ gain of linear differential repetitive processes is presented in terms of linear matrix inequalities （LMIs）. And then the projection approach is applied, which casts the model reduction into a sequential minimization problem with LMI constraints by employing the cone complementary linearization （CCL） algorithm. A numerical example shows the effectiveness of the proposed theory.