广义线性系统全信息反馈调节问题完全参数化方法

Complete parametric approach for output regulation via full information feedback in description linear systems

提出了一种新的求解矩阵方程EΠS=AΠ+BKΠ+BL+P的完全参数化方法。应用该方法和广义逆的基本理论,在不要求系统具有正则性的前提下,给出了反馈增益阵K和L的完全参数化形式。该方法避免了求逆运算和导数运算,具有较好的数值稳定性,克服了以往方法中利用计算机求解的复杂性,给控制器的建立及多目标设计问题带来了极大方便。数值算例验证了本文方法的有效性。

A new complete parametric approach to solve matrix equation EПS=AП＋BKП＋BL＋P was proposed. By using this method and the general inverse theory, and without system regularity condition, a complete parametric expression in the feedback gains K and L were established. This approach can avoid inverse and differential calculations with better numerical stability, reduce the complexity of traditional methods when using computer calculation for the solutions, and provide convenience for the application in controller construction and multi-purpose design problems. A numerical example demonstrates the effect of the proposed method.