On a generalization of the Youla–Kučera parametrization. Part II: the lattice approach to MIMO systems
On a generalization of the Youla–Kučera parametrization. Part II: the lattice approach to MIMO systems
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DOI：
10.1007/s00498-005-0160-9
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发表时间：
2006-08
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影响因子：
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通讯作者：
A. Quadrat
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作者：
A. Quadrat
在Quadrat(即将出现的信号系统)中发展的分析和综合问题的格子方法中，我们得到了内部可镇定的多输入多输出(MIMO)对象的所有稳定化控制器的一般参数化，这些控制器不一定允许双重互质分解。该参数化为自由参数的线性分式变换，并刻画了任意参数的集合。该参数化推广了Quadrat(Syst Control Lett 50：135-148,2003)中单输入单输出对象的参数化方法。它被命名为所有镇定控制器的广义Q-参数化，因为我们表明，本文中提出的一些思想可以追溯到Zames和Francis(IEEE Trans Automat Control28585601,1983)关于∞控制的开创性工作。最后，如果被控对象允许双重互质分解，那么我们证明了广义q-参数化为所有镇定控制器的著名的Youla-Kuč时代的参数化(Desoer et al.IEEE Trans Automat Control 25：399-412,1980；Vidyasagar，控制系统综合：因式分解方法，麻省理工学院出版社，剑桥，1985)。
Within the lattice approach to analysis and synthesis problems recently developed in Quadrat (Signal Syst, to appear), we obtain a general parametrization of all stabilizing controllers for internally stabilizable multi input multi output (MIMO) plants which do not necessarily admit doubly coprime factorizations. This parametrization is a linear fractional transformation of free parameters and the set of arbitrary parameters is characterized. This parametrization generalizes for MIMO plants the parametrization obtained in Quadrat (Syst Control Lett 50:135–148, 2003) for single input single output plants. It is named generalQ-parametrization of all stabilizing controllers as we show that some ideas developed in this paper can be traced back to the pioneering work of Zames and Francis (IEEE Trans Automat control 28:585-601, 1983) onH∞-control. Finally, if the plant admits a doubly coprime factorization, we then prove that the generalQ-parametrization becomes the well-known Youla-Kučera parametrization of all stabilizing controllers (Desoer et al. IEEE Trans Automat control 25:399–412, 1980; Vidyasagar, Control system synthesis: a factorization approach MIT Press, Cambridge 1985).