正规和奇异H∞控制器的统一表达式

给出了一种新的H∞控制器设计方法,通过引入设计时可选的非奇异实数阵,取消了控制器设计时对D矩阵的秩限制.适用于正规的H∞控制问题和奇异的H∞控制问题.对状态反馈等四种典型问题和输出反馈控制问题,给出了控制器存在的充分必要条件.控制器通过Riccati方程的解,用参数化方法表示.输出反馈控制器,通过解两个Riccati方程得到.讨论了控制器的相关特性.

Unified H-infinity controllers of regular and singular plants

A new method for designing H-infinity controllers is given.By introducing regular real matrices,this method has no rank restrictions on matrix D of plants and is suitable for both normal H-infinity control problems and singular H-infinity control problems.The sufficient and necessary conditions of existing appropriate controllers are given for special problems,such as state-feedback control and dynamical output feedback control problem.The controllers are parameterized by the solutions of Riccati(in-)equations.Two Riccati(in)-equations need to be solved for dynamical output feedback control problems.The regular real matrices which can be chosen appropriately in the designing process give more choices in controller.The relationship between our controller and the normal H-infinity controller is discussed.The regular real matrices are chosen for several cases often used.