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基于受限等价变换的结构分析方法,提出实现多个矩阵的同时标准化的方法,从而得到广义系统的标准型,该方法使复杂的广义系统等价于多种简单的系统;根据标准型的特点,对分解后的多种简单广义系统进行细化分类;对不同类型的简单广义系统的控制方法进行研究,使复杂广义系统的控制问题转化为简单广义系统的控制问题。数值仿真结果表明,该方法对广义系统的结构的分类更细致具体,便于后续对广义系统的解、脉冲及其能控等方面进行更深入的研究,理论创新前景十分广阔。
Based on the structural analysis method of constrained equivalent transformation, a method to realize the simultaneous standardization of multiple matrices is proposed, and the standard form of generalized system is obtained. This method makes complex generalized system equivalent to many simple systems. According to the standard The characteristics of the decomposition of a variety of simple generalized systems are refined classification; different types of simple generalized system control methods are studied, the control of complex systems of generalized systems into simple singular systems control problems. The numerical simulation results show that the proposed method can classify the structure of generalized system in a more detailed and specific way and facilitate further research on solutions, impulsions and controllability of generalized systems. The theoretical innovation has a bright future.