The paper presents a novel decoupling method, based on blending the input and output signals of linear dynamical systems. For this purpose, blend vectors are introduced and calculated such that the minimum sensitivity of the controlled mode is maximised, while the worst case gain of the other subsystems is minimised from the blended input to the blended output. The problem is transformed to a standard optimisation program subject to Linear Matrix Inequality constraints. An arising rank constraint is resolved by an alternating projection scheme. The method is presented based on the decoupling of a single mode, but the extension to decouple multiple modes is also discussed. Numerical examples are given to validate the method and to illustrate how the proposed approach can be applied for control engineering problems.

本文提出了一种新的解耦方法，基于混合线性动力系统的输入和输出信号。为此，引入和计算混合向量，使得受控模式的最小灵敏度最大化，而其他子系统的最坏情况增益从混合输入到混合输出最小化。该问题被转换为受线性矩阵不等式约束的标准优化程序。出现的秩约束由交替投影方案解决。该方法基于单模解耦提出，但也讨论了对多模解耦的扩展。给出了数值例子来验证该方法并说明所提出的方法如何应用于控制工程问题。