A metric structure is imposed on state space such that solutions to 1^st order state variable model of a linear system are geodesics subject to restrictions on the system and input matrices. For linear time invariant systems, a 2^nd order state variable model of an extended system to a given 1^st order model is derived. The metric is tailored to systems under consideration.

中文翻译：

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状态空间中系统的度量问题

度量结构施加在状态空间中，使得以1个解决方案^第一线性系统的阶状态变量模型是测地线受试者至系统和输入矩阵的限制。为线性时不变系统，2-^第二扩展的系统给定的1阶状态变量模型^ST阶模型导出。该指标是针对正在考虑的系统量身定制的。