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ON REALIZATION PROBLEM OF LINEAR SYSTEMS OVER COMMUTATIVE RINGS
Author(s): 
Pages: 112-116
Year: Issue:  1
Journal: Control Theory & Applications

Keyword:  交换环主理想整环充分必要条件有限生成模同态线性系统线性输入商模子模线性组合;
Abstract: 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 realizability. 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) = z1 + c1-1z1-1+..... + c1z + c0 ∈R[z] such that over R is calledrecurrent 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 R.
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