线性系统Luenberger能观规范型的充要条件及特征

Necessary and sufficient condition for the realization of Luenberger observable canonical form and its structure characteristics

提出了一种完全能观线性MIMO(multi-input multi-output)系统的能观矩阵的线性无关行向量的搜索方案,并基于此搜索方案提出了一种将完全能观线性MIMO系统化为Luenberger能观规范型的变换矩阵的构造方法。通过对几个定理的证明,阐述了此非奇异变换矩阵与Luenberger能观规范型的关系,提出了将Luenberger能观规范型按照结构的差异划分为广义和狭义2种规范型的观点,并给出了完全能观线性MIMO系统的广义和狭义Luenberger能观规范型实现的充要条件,用3个实例验证了上述观点和方法的正确性和可行性。同时给出了一种方法使得一类不满足Luenberger能观规范型实现条件的线性MIMO系统能够在不改变系统物理结构的前提下变换为Luenberger能观规范型,并通过2个实例的分析和比较对此方法进行了阐述。

An approach is put forward to find the linealy independent vector of the observability matrix of completely observable linear multi-input multi-output（MIMO） system.Based on this approach,a method is advanced to obtain the transformation matrix which can be used for transforming the linear MIMO system to its Luenberger observable canonical form.Through the proving of several theormes,the relation between the transformation matrix and Luenberger observable canonical form is exposited and the Luenberger observal form is divided into two classes,the generalized Luenberger observable canonical form and the special Luenberger observable canonical form,according to its structure difference.The necessary and sufficient condition for the realization of generalized and special Luenberger observable canonical form of completed observable linear MIMO system are given,and three examples are used to verify the correctness and feasibility of the above viewpoint and method.Meanwhile,another method is put forward to transform a class of linear MIMO system,under the condition of unchanging its physical structure,which does not meet the above necessary and sufficient condition,to its Luenberger observable canonical form.Two examples are analyzed and compared to elaborate on the method.