多变量H_∞控制问题的显式解(第二部分,退化情形)

Explicit Solution Expressions of the Multivariable H# Control Problems

5 退化情形的显式解 问题(2)有解的充要条件是Pick矩阵P≥0,其中detP=0时发生了退化,这时P的逆不存在,公式(13)无法使用,需要另作处理,在H_∞最优控制问题求解时,必定出现退化情形,所以退化情形的显式解值得专门研究。P为Hermite矩阵。

This paper gives the explicit solution expressions of the multivariable H∞ control problem in s do-main. The first part gives the unified explicit solution expressions for non-degenerate case from the input and out-put point of view. The second part gives the unified explicit solution expressions for degenerate case which is very important, since the H∞, optimal control is corresponding to the degenerate case. These unified explicit expressions bring convenience to the design of control systems and the research on the properties of the solutions of H∞ control.