| 引用本文: | 李铁钧.交换环上线性系统的实现问题[J].控制理论与应用,1985,2(1):112~116.[点击复制] |
| Liu Tiejun.ON REALIZATION PROBLEM OF LINEAR SYSTEMS OVER COMMUTATIVE RINGS[J].Control Theory and Technology,1985,2(1):112~116.[点击复制] |
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| 交换环上线性系统的实现问题 |
| ON REALIZATION PROBLEM OF LINEAR SYSTEMS OVER COMMUTATIVE RINGS |
| 摘要点击 664 全文点击 363 投稿时间：1982-12-11 修订日期：1983-12-06 |
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| DOI编号 |
| 1985,2(1):112-116 |
| 中文关键词 |
| 英文关键词 |
| 基金项目 |
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| 中文摘要 |
| 本文套路交换环上线性输入-输出映射的实现问题。首先，引入了新的周期性概念。应用这一概念得到了可实现的充分必要条件。然后，讨论自由规范实现的存在问题。证明了，在主理想整环上必存在自由规范实现。 |
| 英文摘要 |
| In the first part of this paper, we introduce a new concept of recurrence for linear input - output map over commutative rings. By this concept, we obtain the necessary and sufficient condition of realizabilit. In the second part of this paper, we discuss the existence of the free canonical realization.
Let R be a commutative ring with identity. The vector sequence a=(a1,a2,???)over Rp is called recurrent if there exists a monic polynomial φ(z)=zl+cl-1zl-1+???+c1z+c0∈R[z] such that
Al+i+cl-1al+i-1+???+clai+1+c0ai=0, i=1，2，???.
A linear input - output map f:Rm[z]→z-1Rp[[z-1]] over R is called recurrent if every f(ei), i=1，2，???,m is recurrent.
The main results of this paper are:
1. A linear input - output map f over R is realizable if and only if f is recurrent.
2. Assume that R is a principal ideal domain, then there must exist the free canonical realization for the realizable input - output maps over . |
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