线性系统的最小实现：“最短基”方法
Minimal realizations of linear systems: The "shortest basis" approach
AI总结：
针对可控离散时间线性系统，提出最短基概念并证明其性质，进而直接从最短基构造控制器规范型和观测器规范型的最小线性实现。
摘要：
给定一个可控离散时间线性系统C，C的最短基是一组具有最小可能长度的线性无关生成元。基B是最短基当且仅当它具有可预测跨度性质（即具有可预测延迟和次数性质，且是非灾难性的），或者等价地当且仅当它具有子系统基性质（对于任何区间J，B中跨度在J内的生成元是子系统C_J的一组基）。C的最小状态空间和最小转移空间的维数分别等于最短基B中在任何给定状态或符号时刻活跃的生成元个数。C的控制器规范型最小线性实现直接来自C的最短基，而观测器规范型最小线性实现直接来自正交系统C^⊥的最短基。这种方法在概念上比经典的最小实现理论更简单。
英文摘要：
Given a controllable discrete-time linear system C, a shortest basis for C is a set of linearly independent generators for C with the least possible lengths. A basis B is a shortest basis if and only if it has the predictable span property (i.e., has the predictable delay and degree properties, and is non-catastrophic), or alternatively if and only if it has the subsystem basis property (for any interval J, the generators in B whose span is in J is a basis for the subsystem C_J). The dimensions of the minimal state spaces and minimal transition spaces of C are simply the numbers of generators in a shortest basis B that are active at any given state or symbol time, respectively. A minimal linear realization for C in controller canonical form follows directly from a shortest basis for C, and a minimal linear realization for C in observer canonical form follows directly from a shortest basis for the orthogonal system C^\perp. This approach seems conceptually simpler than that of classical minimal realization theory.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
