The Fractional Representation Approach to Synthesis Problems: An Algebraic Analysis Viewpoint Part I: (Weakly) Doubly Coprime Factorizations
The Fractional Representation Approach to Synthesis Problems: An Algebraic Analysis Viewpoint Part I: (Weakly) Doubly Coprime Factorizations
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DOI：
10.1137/s0363012902417127
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发表时间：
2003
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影响因子：
--
通讯作者：
A. Quadrat
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文献类型：
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作者：
A. Quadrat
在这篇文章中，我们展示了如何在代数分析框架内重新表述用于分析和综合问题的分数表示方法。在模方面，我们给出了系统允许(弱)左/右/双互质分解的充要条件。此外，我们对整环A进行了明确的刻画，使得每个通过转移矩阵定义的对象-其项属于A的商域-允许(弱)双重互质分解。最后，我们证明了这种代数分析方法一方面允许我们恢复[M.C.Smith，IEEE Trans]中发展的方法。自动的。控制，34(1989)，第1005-1007页]，另一方面，在[K.Mori和K.Abe，SIAM J.Control Opti.，39(2001)，pp.1952-1973；V.R.Sule，SIAM J.Control Opti.，32(1994)，pp.1675-1695和36(1998)，pp.2194-2195；M.Vidyasagar，H.Schneider，和B.A.Francis，IEEE Trans。自动的。控制，27(1982)，第880-894页；M.Vidyasagar，控制系统综合：因式分解方法，麻省理工学院出版社，剑桥，MA，1985]。
In this paper, we show how to reformulate the fractional representation approach to analysis and synthesis problems within an algebraic analysis framework. In terms of modules, we give necessary and sufficient conditions so that a system admits (weakly) left/right/doubly coprime factorizations. Moreover, we explicitly characterize the integral domains A such that every plant---defined by means of a transfer matrix whose entries belong to the quotient field of A---admits (weakly) doubly coprime factorizations. Finally, we show that this algebraic analysis approach allows us to recover, on the one hand, the approach developed in [M. C. Smith, IEEE Trans. Automat. Control, 34 (1989), pp. 1005--1007] and, on the other hand, the ones developed in [K. Mori and K. Abe, SIAM J. Control Optim., 39 (2001), pp. 1952--1973; V. R. Sule, SIAM J. Control Optim., 32 (1994), pp. 1675--1695 and 36 (1998), pp. 2194--2195; M. Vidyasagar, H. Schneider, and B. A. Francis, IEEE Trans. Automat. Control, 27 (1982), pp. 880--894; M. Vidyasagar, Control System Synthesis: A Factorization Approach, MIT Press, Cambridge, MA, 1985].